A Spatial Analysis of the Components of Change of the Housing Stock in England: Will Alternative Means of Adding Dwellings Make a Difference?

Abstract

Whether on greenfield or brownfield sites, new buildings need land. The locations of additional dwellings in England, whether provided through a standard planning process or a light-touch approach, have recently been criticised for not impacting affordability and for being in the wrong places. More sustainable means of raising the stock of abodes in England, including repurposing dilapidated or underused property, land, or infrastructure; reducing the demolition rate; and reducing the time an existing dwelling is left idle, do not consume additional land for building. Although the National Planning Policy Framework for additional dwellings places a duty on each district planning authority to find more land for housing, alternatives to new builds are included in the count. This paper examines the spatial concentrations of the components that can add to the habitable stock of real estate. It examines their take-up over recent years. This is important for land-use planning and the preservation of green spaces in the face of increasing housing pressures. Using a simple, innovative approach to assessing collocation, the paper considers whether there are similarities in spatial concentrations. The approach is used to infer whether builders converting existing property add units in areas where new builds are in more modest supply. Although alternative means of adding to the housing stock may be more sustainable, and more likely to be found in areas of greater need, the numbers are too low to be anything other than a supplement to new builds.

1. Introduction

England has a track record of supplying housing below the need or target rate [1,2,3,4]. One could point to the planning process [1,2,3,4,5,6], the pricing of land [7], monopoly practices amongst builders [8], or the availability of credit [9,10] for increasing amounts of the housing stock becoming unaffordable. It is claimed that increasing unaffordability does not correspond with new supply, so housing is added in the wrong places at the wrong rates. One outcome is that, by a standard affordability measure, London’s house prices have dislocated from the rest of the country [9].

The National Planning Policy Framework (NPPF), published in December 2024, lays out the Labour Government’s annual housing stock expansion target of 370,000 (https://www.gov.uk/government/consultations/proposed-reforms-to-the-national-planning-policy-framework-and-other-changes-to-the-planning-system, accessed on 1 January 2025). This was a considerable increase over the previous Conservative Government’s aim of 300,000, but below some estimates of need [3,4]. The average annual net addition to dwellings over 2012–2013 to 2022–2023 was 207,000. To convert this to a rate, that number is divided by the existing housing stock. England as a whole added 8.38 per 1000 existing dwellings per year over this period. London added 36,600, at a rate of 9.95. The new target requires 15 per 1000 dwellings to be added in England. Although the planned delivery requires planning authorities to release greenfield sites at a greater rate, it recognises the importance of alternative means of increasing the number of dwellings other than new builds. In paragraph 125d and note 50, the NPPF strategy document specifically refers to converting spaces and bringing back into residential use empty homes and other buildings as a means of adding dwellings.

This paper considers four alternative means of boosting the stock of housing. Repurposing includes ‘conversions’ of property that can add more residential homes. Conversion, in the strict sense, entails adapting existing residential properties, whereas change-of-use involves switching non-residential buildings (office, agricultural, and industrial real estate) to residential use or vice versa. It is possible for the net change to be negative. Change-of-use was the focus of additions when the permitted development right (PDR) was introduced. It was hoped to boost repurposing of commercial buildings for residential use [11] in areas where planning agencies appeared unwilling to release sufficient land.

Two more means entail boosting the stock by reducing the flow of withdrawals from the housing market. The number of empty homes is captured by owners reporting that their property has been empty for six months or more (i.e., unoccupied and unfurnished) for the purposes of assessing a local council tax liability. Reducing the long-term vacancy (LTV) data can be viewed as increasing the number of usable dwellings outside of the planning process. Demolitions imply removing housing, whether it be functional or not, from stock. Lowering the demolition rate, when combined with renovation, could increase the useful housing stock. How these four alternatives to new dwellings are distributed across space could be important for policymakers who see a mismatch between the location of new builds and need.

This paper examines the recent record of adding dwellings to the English housing stock in accordance with the NPPF. In particular, it explores where there are concentrations of types of additions. Questions asked include the following: Are clusters of different types of additional dwellings distributed across space in a similar fashion? Do the clusters of different types of additional dwellings reflect proxies for market pressures? Extended territories of concentration or deficiency for each of the components of additional dwellings are analysed as if they reflect market forces. House price/earnings ratios (HPERs) indicate house purchase pressures or, as the NPPF asserts, excess demand for dwellings. Rates of local authority/council waiting lists indicate pressures in the renting market. A high vacancy rate could signal low demand, which could be accompanied by a high demolition rate. Both of these should correspond with weak provision in new builds.

The paper is constructed in seven sections. First, there is an outline of how the components of housing stock change can be envisaged. Second, there is a review of perspectives on the dwelling additions problem in the English context. The methods of assessing spatial concentration and agreement are presented third, followed by data. The fifth section entails findings. A discussion of the findings and conclusion follow.

2. Theoretical Framework

2.1. The Monocentric Model and Variations

A useful framework for discussing affordability, need, land prices, house prices, rents, and the location of new builds in the absence of planning is the monocentric urban model of rents, as presented by [12]. They posit that with homogenous dwellings, house prices decline with distance from the central business district (CBD), even with a homogeneous income level, which is determined by the productivity level at the CBD. On that basis, affordability, as defined by rent or price divided by income, declines with distance from the CBD.

A rise in productivity in one CBD leads to greater competition for dwellings in that urban area, resulting in a rise in price. The supply of housing will be a function of price [12]. The new builds will be constructed at the city boundary, changing the use of green/agricultural land to residential land. The land rent at the boundary will be a function of its agricultural use. The price of land will be the present value of the rent based on the cost of capital. Land price is derived as a residual from house price. House prices at the border will be based on the land price and the cost of converting the land to residential housing, also discounted by the cost of capital. The developed land for all other dwellings will have a locational premium buried in their higher house price, with a maximum at the boundary with the CBD. The land price and house price are affected by the expected growth rate of the city. Housing will experience an enhanced locational premium as the city expands. As the city expands, land close to the boundary is absorbed, switching uses, and subsequently earns a location premium.

Assumptions of the monocentric model can be relaxed to produce a more applicable framework. There could be speculation on the use of greenfield-site land beyond the city border. A landowner could develop a site before the city boundary crossed their site. Or a landowner could retain the land as vacant once the boundary has crossed their land, seeking to extract a locational premium later. Land could be used more intensively so that smaller dwellings and/or taller building can be constructed where land is more valuable. Rather than solely distance to the CBD, locational amenities also feature in a spatial equilibrium model [13].

McCann [14] posited four income groups. The rich outbid others for dwellings closer to amenities [15]. They outbid others for larger dwellings at the edge of a housing market area, drawn by the attraction of lower-density space [16]. Poorer groups that rely on local authority (public or council) housing, [14] posits, will be constrained to be closer to the city centre than other groups by the public transport network. Rather than using price rationing, which is beyond those that are eligible for social housing, dwellings will be allocated by a complex queuing system, for which there will be waiting lists.

A components-of-change structure is presented by [17]. Such change can be seen in the light of a supply curve of dwellings discussed by [12]. Absentee landlords derive returns from providing dwellings services to tenants. Rent is assumed to be higher for a larger property, as are costs such as maintenance and interest payments on the mortgage. With a rise in demand for dwellings in the local area, the following may occur:

• The representative landlord could commission the construction of a new dwelling. Modelled as being part of an upward-sloping portion of a supply schedule for dwellings in the medium-term, this is classified as a new build in the components of change;
• A dwelling could be bought from the owner–occupier market. Adding demand to the complementary market implies rent and price movements are linked by this shift;
• The dwelling may be remodelled. By converting a house into two flats, the number of dwellings per m² increase, intensifying land use. Globally, this increases the number of dwellings by one, resulting in a net increase through conversions;
• Conversion of property, such as offices and retail spaces, from non-residential to residential use may occur. Converting a house from a shop increases the number of dwellings. This is captured as a positive net increase through change-of-use.

With a leftward shift in the demand for dwellings locally, the housing stock is posited to remain unchanged [18,19]. Although there will be a point where new construction is not viable [18], as long as landlords cover their average variable costs, the property will ‘participate’ in the market (or be inside it) in the very short run. In the context of the above, the supply of residential properties could be reduced by the equivalent switching of points 2–4 in the reverse direction. Glaeser [19] posits that the durability of housing results in a supply curve that is kinked, with the steep/vertical portion reflecting no new construction. Indeed, with the stock unchanged and falling demand, rents drop. Declining cities attract those of more modest means to benefit from lower rents.

O’Sullivan [17] emphasises maintenance costs. Expenditure on depreciation will increase with time. How assiduously the landlord maintains the dwelling will affect the length of its life cycle. The landlord is posited to increase maintenance expenditure on the property when the housing asset has higher expected returns, increasing the time to demolition or more generally lowering the local demolition rate. The obverse is the case with a leftward demand shift to the point where the landlord could suspend such maintenance payments. Once average variable costs are not covered, there are the following options:

5.

Temporarily withdraw the dwelling, waiting for the market to improve. This could be captured by short-term vacancy data;

6.

Leave it vacant on a persistent basis. This could be captured by long-term vacancy data. A local tax regime could favour long-term vacancies, exempting the property from local taxes. Recent UK governments have sought to impose taxes on long-term vacant dwellings and second homes to deter such uses;

7.

Abandonment is a logical outcome of 6. However, in the British system, the mortgage debt obligation remains with the landlord, whereas in other jurisdictions ownership could revert to the mortgage lender and the debt be written off. Options five, six, and seven put the dwelling outside the market, unavailable to be rented.

Demolishing the dwelling is an alternative choice to 6 and 7. Couch [20] consider the demolition of the least popular housing stock and its replacement with housing that more closely meets contemporary demand as the most successful policy in tackling housing vacancy in Liverpool. Power [21] is critical of less sustainable approaches in such situations, arguing against demolition and claiming that renovation is not only feasible, but it is essential for the regeneration of mature areas. Demolition imposes severe social costs both on the communities that are targeted for regeneration and on the wider urban environment. Adding in the cost of delays in reusing the land, the loss of housing capacity, and the infrastructure cost of new housing, demolition is almost never justified in total cost terms. Estimates of such market costs are available. For example, one can get a feel for the costs of remodelling housing services in 2024 from artisan websites. Checkatrader estimates that the average cost of building a three-bedroom house (typical size 90 to 120 m²) falls in the range £126,000 to £300,000. Demolishing a similar-sized dwelling (80 to 120 m²) falls in the range £5600 to £12,000. This is when the average house price in the UK is £300,000. Checkatrader again can offer estimates on the renovation costs of a 3-bedroom house (£43,530 to £110,350).

Adding to the lower tail, demolitions and long-term vacancies fit the suggestion of an S-shaped supply curve. However, using the land more intensively (3) could result in demolition in areas where there is new construction. As such, the density of demolitions could be in both high- and low-demand housing market areas.

2.2. Land for Building Sites

England has a land area of just over 13,046,000 hectares. Greenbelts around the key cities of England cover 1,634,760 hectares, which constitutes an eighth of the land area of England (https://www.gov.uk/government/statistics/local-authority-greenbelt-statistics-for-england-2021-to-2022, accessed on 1 January 2025). When including land also protected against development by other designations, 4.9 million hectares (37.4%) of England are subject to some restriction.

Land that has been occupied by a permanent structure and any fixed surface infrastructure associated with it for building purposes is called a brownfield site. Previously developed land excludes the land housing or that housed agricultural or forestry buildings and land that has been restored but previously was developed for minerals extraction or waste disposal by landfill. Greenfield sites have not been developed before, except in the above cases. Greenfield land accounts for 91.1% of land across England and brownfield land accounts for 8.7% of land. In 2021–2022, 54% of all new homes were built on brownfield land and 46% on greenfield sites.

Local Planning Authorities are discouraged from releasing land for building within greenbelts, unless there are exceptional circumstances, so as to restrain urban sprawl. That said, 6.8% of land within greenbelt areas is developed. In 2021–2022, new houses built on greenbelt land made up 2.5% of the total, of which 51% were built on brownfield land and 49% were built on greenfield land, broadly in line with non-greenbelt land uses. NPPF includes plans for grey belt usage (https://www.local.gov.uk/sites/default/files/documents/Dec%2024%20NPPF%20Webinar%2019%20March%20Golden%20Rules.pdf, accessed on 1 January 2025). A grey belt is land in the greenbelt comprising previously developed land and/or any other land that does not strongly contribute to any of the purposes that a greenbelt might have. It is not clearly differentiated from a brownfield and is understood to include poor quality and ugly land use in greenbelt areas. The grey belt would be released for development before the greenbelt.

2.3. Land for the Least Able to Pay

Barker [1] was also concerned about publicly funded housing for those who need it. In England, 72,000 affordable houses were completed in 2021–2022, accounting for around 29% of all completions. The construction of these homes is typically undertaken by a public body (such as Homes England) or a Registered Housing Provider, a housebuilder regulated to build social housing. Housing Associations and local authorities fund the construction of social-rented homes. Between 2012–2013 and 2022–2023, 93,875 were added to total dwellings. These dwellings are targeted at those that live in overcrowded or very bad conditions or are homeless with limited means (https://england.shelter.org.uk/housing_advice/council_housing_association/how_to_apply_for_council_housing/who_can_join_the_housing_register, accessed on 1 January 2025). There were 1.28 million households (or 5.2% of all households) on local council waiting lists for such a social home. Despite the additions to overall dwellings, 212,590 social homes were sold and a further 58,772 were demolished, resulting in a net loss of 177,487 social-rented homes over the 11 years (https://www.crisis.org.uk/about-us/media-centre/over-12-000-social-homes-lost-last-year-as-over-one-million-households-remain-trapped-on-council-waiting-lists/, accessed on 1 January 2025). This should be seen in the context of around four million social-renting households. Waiting lists offer a non-pecuniary view of housing pressures for those who are of very modest means, who are possibly restricted to live in a certain locale close to the CBD [14]. A long queue is viewed here as a measure of a shortage of affordable rented accommodation. Mahmoud [22] sees land prices as a key concern, particularly for this group. With a large reduction in the central government’s capital grant for social housing in the three years up to 2010, land acquisition costs played a greater role in the viability of social housing. Between 2011–2012 and 2014–2015, the top 10% of district authorities where land was most expensive saw a 70% drop in the numbers of new affordable/social-rent homes, while the rest of England experienced a fall of 20%. Assuming the land is close to the CBD, the locational premium will be high, which will be greater in high-productivity centres. This would be most acutely felt by boroughs in London. One means of avoiding paying the locational premium is for government departments to look to their own land banks. Beswick [7] is critical of the selling-off of public land for housing. Since 1979, 10% of the British land mass has been passed from public to private hands, such as in the form of the NHS or the Ministry of Defence disposing of land. The research shows that 43% of the housing capacity from public land sales between 2011 and 2019 was in London and the South East. The public choice was stark in Greenwich, Newham, Tower Hamlets (London boroughs), Medway (South East), Birmingham, and Manchester, which were in the list of the top 20 areas with housing capacity on public land sold. They are also in the top twenty local authorities in terms of housing waiting lists. Hoping that the private sector would use this land for affordable housing was found to be optimistic. Only 6% of homes built on surplus central government land was for social-rented housing in this period, which was genuinely affordable. In March 2025, there was another public land sale (https://www.gov.uk/government/news/public-land-unlocked-for-the-next-generation-of-home-owners, accessed on 1 January 2025) where claims were made about the delivery of housing for hard-working people. This included land from Network Rail.

The UK’s history is not unique. Social housing as a share of total housing within the European Union has declined steadily over the last decade, dropping three percentage points to 8% in 2021 [23]. Coastal cities and tourist destinations also experienced a rapid rise in rents and housing prices. In many regions, the high percentage of vacant houses (including holiday homes) and short-term rentals puts further pressure on the housing market. Indeed, over 20% of homes in Portugal, Spain, Malta, and Estonia are vacant [23].

2.4. Bidding for Land

The Competition and Markets Authority launched an investigation into the housebuilding market in 2023 to explore whether monopoly practices would lead to significant under-delivery relative to a socially desirable level, especially in London, the South East, and the East of England. It characterised the construction market, in the main, as speculative. Around 141,000 (around 60%) of the 239,000 new-build homes completed in Britain in 2021–2022 fall into this category [8]. Under the residual valuation model, housebuilders bid for land based on their estimate of the value of the homes they can build on it [12]. Housebuilders devote effort to acquiring these essential raw materials well in advance [23]. Builders’ incentives to pursue the strategy of maximising sales prices are reinforced by the way they compete to purchase developable land. Where land is released in small, spatially distinct packages, potential competition for the dwellings constructed on the land is restricted, so that builders have higher expectations of house prices, and they will bid more for the land.

The number of new homes available to be sold at any one time is limited in the UK, reflecting a certain stable pace of development—the build-out rate [8,24]. Housebuilders tend to build at a rate that is consistent with the local absorption rates, i.e., the rate at which houses can be sold without needing to reduce their prices. Increases in demand are reflected in price rather than output. Decreased demand is addressed through incentives and increased marketing, rather than by cutting production. The CMA do not find this to be a restrictive practice.

2.5. Planning and the PDR

It is common to raise the issue of the planning process [1,2,3,4] as the key problem in the housing conundrum. In paragraph 4.201, CMA [8] observes that builders are reliant on permission being granted for construction to take place. Under the Conservative administration, English land-use planning was devolved to local authorities, who had their own local development plans and estimates of future housing need. The Localism Act, 2011 resulted in local vetoes on plans being a significant problem [25]. Breach [5] also points to this constraint, which forces the concentration of new homes to be in the centres or on the very edges of these cities. From 2011 to 2019 the majority of neighbourhoods outside city centres failed to build much in the way of new houses, possibly less than one home a year. Almost half of the suburbs located near rail, tram, and tube stations built less than one new house. To avoid being clogged in the planning system, builders are disincentivised from choosing locations with high rates of planning objections [5,6].

On a regional basis, restrictions imposed by planning authorities in the less affordable South East of England region are more restrictive than those in the North East of England [26]. The resulting constraint pushed prices to be roughly 33% higher in 2008 in the South East. Again, England is not unusual. In the US [27], statewide (regional) regulations on sprawl and building heights account for an increase in average price of USD 73,000 in Vancouver and USD 203,000 in Seattle. Hsieh [28] argues that housing supply constraints in high-productivity cities reduce the growth of national product. It is recognised in Europe generally that there is a regulatory barrier issue [23]. The EIB estimates that the 2023 construction rate of new dwellings should have been 70% higher to meet the additional demand in 2025. Obtaining building permits is slow and time-consuming. Making vacant land available for urban development and reducing obstacles to densification are advocated.

The Conservative administration of the 2010s sought to bypass local planning restrictions with the introduction of the PDR. While developers in England were previously required to submit detailed plans and apply for full planning permission for change-of-use, the changes meant they only had to notify the local planning authority of such a modification [11]. When they were introduced in England in 2013, change-of-use orders under PDR for office, agricultural, or industrial conversions created 12,500 dwellings. Over the next 7 years, change-of-use contributed 172,000 additional dwellings. The majority of PDR conversions in England have been small-scale (below 10 units) and 89% are office conversions. By comparison, over the same 8 years, there were 39,000 conversions (of existing dwellings). However, net new builds (new builds over demolitions) were six times the contribution of the two categories of building repurposing over the eleven years between 2012–2013 and 2022–2023. Over the long term, the number of permissions granted were insufficient to support housebuilding at the level required to meet the 300,000 target [8].

Canelas [29] argues that the rationale of regulatory light-touch ‘smacks of a pro-market ideology’, where the market will provide, both in terms of the number and quality of additional dwellings. The deregulation of office-to-residential conversions in England has significant limitations in terms of delivering policy objectives, as defined both centrally and locally [29]. PDRs inadequately deal with the different dwelling issues experienced by distinct local real estate markets. The experience of change-of-use overseas is different. In the Netherlands, soft power is exercised [29]. An elected member of the city council, responsible for planning, would proactively approach owners of vacant buildings to discuss their potential for conversion, and would also help developers navigate through regulations.

Comparing London with Italian office-to-residential conversion [30] makes two related points. Unregulated schemes in England mean that many buildings are brought forward that should not be. Secondly, the Italian regulated scheme covers health and hygiene within broader urban quality objectives, resulting in high-quality outcomes. It is not conversion that is the problem in England. In the absence of guidance, PDR developers build sub-standard homes. Additional dwellings brought through the PDR route are not impacting affordability. Indeed, the claim being made is that the wrong type of housing emerges in the wrong places [30], p. 20. PDR offers no solution to the affordability crisis and is not intended to.

The benefits of a planned transformation within a tight urban space are outlined by two cases of Nature-based Solutions (NbSs) through the EU’s URBAN GreenUP project [31]. NbSs are cost-effective, simultaneously provide environmental, social, and economic benefits, and help build resilience. For inner cities these benefits can include moderating noise and air pollution. It has been concluded that residents appreciate proximity to public and green spaces that offer environmental benefits. It is acknowledged that the only solution to richer groups outbidding others for access to enhanced spaces is for housing rents to be subsidised. This is unlikely to be supported in the UK.

The campaign group Empty Homes [32] is most closely associated with residential dwellings that are classified as long-term vacant in Britain. It also considers the benefits of encouraging greater use of empty commercial space to address housing need, or change-of-use (https://static1.squarespace.com/static/6553693f7d629a133b6a4ece/t/65f2b23f8f6c7644f4e9d6b5/1710404161917/REPORTAffordable-homes-from-empty-commercial-spaces2016.pdf, accessed on 1 January 2025). Before the PDR took off, it highlighted cities such as Leeds, Manchester, and Nottingham as having the greatest office vacancy rates in 2014, whilst the North East region had the highest retail vacancy rates.

2.6. Planning Staff

The Planning Inspectorate, following the Localism Act 2011, was still charged with interpreting and implementing government policy, but with the removal of strategic-level plans. Local development plans were the responsibility of local councils. Their decision-making was subject to a greater degree of legal scrutiny and challenge. So, the Inspectorate had more work [25]. This was made worse by funding. Ref. [33] reported that between 2010–2011 and 2017–2018, there was a 37.9% real-terms fall in net current expenditure on local authorities’ planning functions. They struggled to produce local housing plans and to hear appeals, due, in part, to a reduction in staffing.

2.7. Affordability and Credit

One measure of home ownership affordability is captured by HPERs. Over the 2009–2019 period, ref. [9] finds that the district HPER rank-order is stable, but the less affordable districts saw more rapid growth, especially the London area. Declining cities in the north, such as Sheffield, Liverpool, and Newcastle, are surrounded by rural areas that become relatively affordable. Sparsely populated areas, such as rural Wales, Cornwall, and East Yorkshire, also do not ‘keep up’. The divergence in HPERs is related to productivity in general and the self-sorting of workers across space in particular, with a concentration of higher long-term earners in a very fluid, extended London market [9]. To the lender, the default risk for these characteristics would be such that they are willing to be flexible on lending criteria, operating on higher income lending multiples. This implies that HPERs may be a function of a risk assessment of the borrower rather than the best indicator of housing demand. Szumilo [10] sees a problem with rising HPERs. He also analyses English local authority district data. He sees the management of demand as well as supply as the route to address ownership affordability.

2.8. Applications of Spatial Autocorrelation Methods

When analysing vacant dwellings in the City of Sapporo, Japan [34], Getis–Ord Gi* statistics are used. A cluster of grid squares can be viewed as a hot spot if the number of vacant dwellings is distributed across space in such a way that the cluster has an above-average number of vacancies. Van [34] examine factors associated with each of the three zone types (hot, cold, and random) in partial least squares analyses. Children have a positive, and home ownership a negative influence on the number of vacancies. Interestingly, the number of elderly had a positive impact on hot spots but a negative impact on cold and random spots. The hot spot revealed comprises the CBD, in the sense of a monocentric urban model, plus neighbouring areas. Meanwhile, cold spots are located mainly in the fringe districts. The residual random areas lie between the hot and cold spots. The research notes that public housing has a high vacancy rate. This is attributed to the old age and sub-standard nature of the housing. Importantly, the houses are undersized, failing to suit the needs of modern life. High-density offices are located in the centre of the business district, where the dwelling price can be excessively high. The central districts have increased in population whilst the suburban population has declined in recent years, suggesting that the vacancy hot spot is not consistent with a declining population.

Gao [35] also used Gi* statistics to reveal hot spots of dwelling abandonment and demolition in Germany (Dessau) and the US (Flint). The concentration map of Dessau has one large hot spot in the centre and four cold spots in its peripheral area. Flint has several hot spots scattered over a relatively large area. They describe Flint’s pattern as perforated and Dessau’s as a doughnut. The Dessau demolition hot spots can be explained by planning, where the authority shifted tenants from lower- to higher-occupation buildings. In the process, recreational amenities were added. Indeed, not only did Flint struggle with arresting abandonment, but it also had difficulties repurposing vacant homes.

Guillain [36] uses Anselin’s alternative to Gi*, the local indicator of spatial autocorrelation (LISA). Alongside hot spots (high–high combination) and cold spots (low–low combination), there are high–low combinations, diamonds-in-the-rough of a relatively high density of employment surrounded by low-value territories. A low–high combination or doughnut pattern is a low-observation territory with neighbours that have high values. The research reveals a HH combination core surrounded a low–low periphery in the Ile-de-France area. High–low combinations are found in the periphery. Exploring the distribution of GDP/head in 138 regions in Europe over the 15 years from 1980, Ref. [37] found European regions to be stratified over time: rich regions surrounded by rich neighbours; poor regions have poor neighbours. Gray [38] uses LISAs of migrants of various age groups and affordability, showing how children and those 30–39-years of age relocate to a ring of districts outside London.

3. Methods

There are two stages in the analysis. First, each areal unit (district) is allocated to one of three classifications for each of the k dimensions of housing using a spatial autocorrelation method. The second stage of the analysis is to utilise the classifications at the first stage to explore their correspondence across dimensions and over time using a measure of agreement. The agreement coefficient provides a measure of how well spatial autocorrelation classifications correspond or align across two or more variables. Put simply, the map of hot and cold spots at stage one for two or more dimensions of housing (new builds, change-of-use, conversions, demolitions, and long-term vacancies) is assessed for agreement. The housing dimensions are also assessed for agreement with affordability and waiting lists.

3.1. Spatial Autocorrelation

A variable is spatially random if it is distributed following no discernible pattern over space. Spatial autocorrelation implies that the spatial randomness hypothesis is rejected. Positive spatial autocorrelation occurs when similar values tend to group together in locations that have are contiguous or in close proximity beyond what would occur randomly; negative spatial autocorrelation occurs in cases where similar values tend to be dispersed and further apart from each other. Moran’s I is commonly used to test the null hypothesis of spatial randomness. Spatial autocorrelation involves correlating a variable with the spatial weighted average of itself. Moran’s $I={\displaystyle \frac{N{{\displaystyle \sum }}_{i=1}^N{{\displaystyle \sum }}_{r=1}^N\left(x_i - \overline{x}\right)\left(x_r - \overline{x}\right)w_{ir}}{{{\displaystyle \sum }}_{i=1}^N{{\displaystyle \sum }}_{r=1}^N{w}_{ir}{{\displaystyle \sum }}_{i=1}^N{\left(x_i - \overline{x}\right)}^2}}$, where $\overline{x}$ is the mean of all the values in X. x_i is the value associated with district i.

The value of I depends on how ‘local’ or spatial proximity is envisaged and is represented by a weights matrix, W. A queen weights matrix is contiguity-based, where aerial units (districts) have common borders and so are neighbours. If district r has a border with district i, the weight w_ir = 1 in matrix W. If they do not have a common border, the weights value is 0. The requirement for contiguity would preclude an aerial unit (district) from being classified as part of a cluster if it has no neighbours. An island with only one district has a weight of zero for all weights in the matrix. The Isle of Wight is the only case in England’s set of districts. The matrix is adapted so that w_ir = 1 in the case of the two nearest neighbours (New Forest and Gosport). As such, these two districts are treated as contiguous with the Isle of Wight for assessing clusters, despite being separated by the Solent River.

The overall global value of I has a range and interpretation much like Pearson’s correlation coefficient. However, Moran’s I does not indicate where these clusters are located. To address this, Getis–Ord Gi* is used. $G_i^{\ast }={\displaystyle \frac{{{\displaystyle \sum }}_{r=1}^N{w}_{ir}{x}_r-\overline{x}{{\displaystyle \sum }}_{r=1}^N{w}_{ir}}{\sqrt{\frac{N{{\displaystyle \sum }}_{r=1}^N{\left(w_{ir}\right)}^2-{\left({{\displaystyle \sum }}_{r=1}^N{w}_{ir}\right)}^2}{N-1}}\sqrt{\frac{1}{N}{{\displaystyle \sum }}_{r=1}^N{\left(x_r-\overline{x}\right)}^2}}}$ generates three zones. A hot-spot combination comprises a centre and neighbouring areas. This spatial concentration of districts is deemed a cluster with high values of a housing dimension. A cold combination highlights a cluster of the obverse. There can be one without the other. The third group comprises those that are not located in a spatially distinctive area and are classified as random or not significant.

As Geoda’s online guidance shows (https://geodacenter.github.io/workbook/6a_local_auto/lab6a.html, accessed on 1 January 2025), it is useful to ‘link’ maps so that clusters covering districts generated using one variable can highlight those same districts in another map, displaying a spatial distribution of a different variable. If the linking was between two maps of clusters associated with a common activity, such as with house construction, it may be appropriate to consider the extent of cluster overlap. For instance, if there is an increase in demand for dwellings nationally, but the local effect is not uniform, the outcome could entail hot spot(s) for construction of new dwellings which overlap with those for conversions. Observing that two maps have a similar distribution of clusters calls for a measure of matching or agreement of territory classifications which could be either global or cluster-oriented. It is this area in which this paper is situated.

3.2. Fleiss’ Kappa

From stage 1, each district has a classification of either Hot, Cold, and random (not significant) for each of the k housing dimensions explored for agreement. Fleiss’ kappa coefficient (κ) measures inter-rater reliability. In this context, kappa measures the agreement between k dimensions of housing. The proportion of districts to be allocated to the jth category is $p_j={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^N{n}_{ij}}{Nk}}$, where n_ij is the number of times the ith district is found in the jth classification. Given that there are m possible classifications, if the districts were randomly allocated to a classification, the expected agreement rate across all districts would be $P\left(E\right)={{\displaystyle \sum }}_{1=j}^m{p}_j^2$. The proportion of times the districts are assigned the same category is $P\left(A\right)=\left[{\displaystyle \frac{1}{Nk\left(k-1\right)}}{\displaystyle \sum }_{i=1}^N{\displaystyle \sum }_{j=1}^m{n}_{ij}^2\right]-{\displaystyle \frac{1}{k-1}}$. The global kappa statistic is $\kappa ={\displaystyle \frac{P\left(A\right) - P\left(E\right)}{1 - P\left(E\right)}}$. Also, κ_j, the individual kappas, are measures for each of the cluster classifications separately against all other categories combined, such as kappa κ_j = $1 - {\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^N{n}_{ij}\left(k - n_{ij}\right)}{Nk\left(k - 1\right)p_j\left(1 - p_j\right)}}$.

Guidance on how to interpret a kappa value is found in [39]. Agreement is classified on a rising scale as slight in the range above 0 to 0.20; fair at 0.21 < 0.40; moderate at 0.41 < 0.60; substantial at 0.61 < 0.80; and in almost perfect agreement at >0.81. Zero is the agreement that would occur by chance. A negative value indicates that agreement is lower than would be expected by chance. This is classified as poor agreement but could be viewed as disagreement. Overall, κ will be a weighted average of all κ_j.

4. Data

The data is drawn from UK Government statistical services that are freely available public sources. They are at the local authority district level. The district level is an administrative territory below that of a region, often delineated by the ‘built up’ area of a node or rurality with low-density housing. The UK’s Department for Levelling Up, Housing and Communities (DLUHC) hosts data on additional dwellings (Table 123: net additional dwellings, component flows of, by local authority district, England, 2012–2013 to 2022–2023), the total number of dwellings, dwellings vacant (Table 615: vacant dwellings by local authority district: England, from 2004), and the number of households on housing registers (or waiting lists) (Table 600: Number of households on local authority housing registers (waiting lists)). The components of additional dwellings reported that feature here are new builds, change-of-use, conversions, and demolitions. Population estimates (https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationestimates/datasets/analysisofpopulationestimatestoolforuk, accessed on 1 January 2025), house price–earnings ratios (https://www.ons.gov.uk/peoplepopulationandcommunity/housing/datasets/ratioofhousepricetoworkplacebasedearningslowerquartileandmedian/current, accessed on 1 January 2025), and the electronic map (https://geoportal.statistics.gov.uk/search?q=MAP_CTY_LAD&sort=Date%20Created%7Ccreated%7Cdesc, accessed on 1 January 2025) can be drawn from the Office for National Statistics (ONS). The map offers the spatial area of each district.

The data runs from 2012–2013 to 2022–2023. The nature of change-of-use and demolitions at a disaggregated level is such that there can be intermittent cases, which, if analysed on a yearly basis, can lead to over- or underrepresenting the activity in certain districts. To address this, the data is averaged over eight periods before the year 2020 or 2020–2021 for the pre-COVID-19 analysis, or over the two periods after. The year in between is omitted due to the unusual impact on economic activity of COVID-19.

Analyses of data sets comprising values for aerial units that are not uniform require some standardisation. There are i districts of various sizes, i = 1 … N H_i is the stock of housing in district i, and B_i is a housing dimension. With stock measures, the larger the geographic size of district i, the greater the B_i, ceteris paribus. The ratio B_i ÷ H_i is a housing dimension rate. H_i = the number of dwellings that existed in 2020 in district i. The following variables are converted to rates in the manner indicated: new builds; change-of-use; conversions; long-term vacancies; demolitions; and waiting lists. The rate is multiplied by 1000 to produce, in the case of new builds, the average number of new builds ‘per 1000 dwellings’ for the period before COVID-19 and after COVID-19. The population density is calculated by dividing the district population in 2020 by the geographical area of the district and converted to 1000/km².

Long-term vacancies are dwellings that are reported as being empty for six months or more (i.e., unoccupied and unfurnished) for the purposes of council tax. The house price–earnings ratio is derived by dividing the estimated average house price at the lower quartile and dividing that by the earnings at the lower quartile for the district concerned. The National Housing Planning Advice Unit [40] uses the ratio in the lower-quartile form as a measure of affordability for first-time buyers. As commuting into London from the surrounding East of England and South East is extensive, gross earnings (used to generate the HPER) will vary in size, depending on how they are calculated. The earnings are workplace-based (where people work) rather than residence-based (where they live). They feature only full-time employees on adult rates of pay. The HPER ratios do not need adapting further as they are directly comparable across differently sized districts.

The length of a waiting list is viewed here as a measure of affordable rented accommodation for those in the renting market. There will always be a waiting list flow: some join whilst others leave. If the average length of the list rises, it is taken that there is a tighter housing market. As with other standardisations above, to account for differing local authority sizes, the number on the list is divided by the number of dwellings.

Excluding the Isles of Scilly, which has intermittent data, the analysis features 308 districts. A subset of these (180) (https://www.gov.uk/government/statistics/local-authority-greenbelt-statistics-for-england-2021-to-2022, accessed on 1 January 2025) districts have some measure of greenbelt restricted land within their domains. From here on, these 180 are described as greenbelt districts, which control planning permission over 46% of the English land mass. The data runs from 2012–2013 to 2022–2023. The data period is selected based on the reporting of change-of-use.

5. Findings

5.1. Context

The population density in England in 2020 was 431.78 persons/km². When calculating the population density by district, the median and mean are notably higher than that (742/km², 1813/km²), indictive of highly skewed data. With an emphasis on built-up areas, it is common for urban districts to be much smaller than the neighbouring rural ones. Districts are broadly classified as Predominantly Urban (58%) and Rural (42%) by DEFRA. The former has a median and average density of 2647 and 3545/km², respectively, whilst the latter has values of 308 and 588/km². A housing market area is unlikely to correspond with an administrative boundary. The discussion of the monocentric model in Section 2 highlights that richer groups may seek lower-intensity land-use spaces yet still be in a housing market linked to the local node by commuting [10], which traverses the urban–rural boundary. The greenbelt districts have a median and average density of 1069 and 1711/km², respectively, whereas non-greenbelt districts have values of 369 and 1955/km², respectively. The greenbelt density is more in line with that of a built-up area than a rural one.

To provide some context using hot and cold clusters, population density and House Price–Earnings ratio cluster maps are displayed in Figure 1. The population density indicates only one centre, an extended London hot spot. The cold clusters should demark the less-populated rural areas. The random zone should contain towns and less-dense urban areas. This procedure is not unlike Guillain et al.’s [36]. London boroughs have the greatest densities and are collocated. Other cities should emerge as a series of hot spots but do not. This is, in part, related to London’s size and unusual nature. The city districts of Birmingham and Manchester are aerial units which, although they use land intensively, have densities half that of the 10th most dense district in London.

A spatial correlation coefficient estimated using a queen matrix assesses territories with common borders and aligned values. A population density map would feature built-up areas surrounded by rural areas. If the map was of clusters, a node defined as a single local district would show as a yellow void within a cold zone. This is rare in Figure 1, suggesting that it is not unusual for nodes defined in this way to have a population density not significantly dissimilar to the surrounding areas.

Through commuting across the urban–rural divide [16] a rural area’s HPER can be higher than that of a local urban area [14]. Indeed, HPERs for the city are lower than non-city (smaller nodes and rural) districts in the north and Midlands of England. London has the greatest HPER [9]. The HPER map reveals the London area as a hot spot, whilst cold zones cover much of the north of England plus the Midlands. Lincoln, Hull, Nottingham, and Preston, which have lower HPERs than their rural neighbours, show up as yellow voids.

A review of the medians and relative spreads based on each housing dimension’s classification is presented in

Table 1. Cluster and group activity rates. NS = Not Significant; Δ of Use = Change-of-Use; LTVR = long-term vacancy Rate, CoV = Coefficient of Variation; QoV = Quartile Coefficients of Variation; GnBt = Greenbelt Districts; Not GB = Not Greenbelt Districts.

		New Build	Conversion	Δ of Use	LTVR	Demolition
	Median	6.21	0.12	0.86	0.78	0.27
	Not GB	7.2	0.12	0.85	0.78	0.24
	GnBt	5.85	0.11	0.86	0.78	0.32
NS	CoV	0.431	1.147	0.601	0.389	0.895
	QoV	0.287	0.556	0.391	0.247	0.629
	N	105 + 152	108 + 149	99 + 144	98 + 106	90 + 149
	Median	8.97	0.31	1.39	1.30	0.38
	Not GB	8.18	0.3	1.13	1.43	0.43
	GnBt	10.57	0.45	1.43	1.29	0.32
Hot	CoV	0.380	0.737	0.981	0.336	0.622
	QoV	0.295	0.526	0.344	0.221	0.347
	N	20 + 17	9 + 14	10 + 17	14 + 34	12 + 16
	Median	4.74	0.1	0.53	0.63	0.16
	Not GB	4.61	0.13	0.41	0.62	0.13
	GnBt	4.79	0.08	0.62	0.65	0.30
Cold	Cov	0.571	0.797	0.814	0.335	0.817
	QoV	0.432	0.595	0.434	0.197	0.600
	N	3 + 11	11 + 17	19 + 19	40 + 16	26 + 15
	Median	6.44	0.12	0.86	0.80	0.27
	Not GB	7.25	0.13	0.81	0.78	0.24
	GnBt	5.87	0.12	0.88	0.83	0.32
All	Cov	0.443	1.141	0.757	0.456	0.885
	QoV	0.299	0.558	0.427	0.283	0.618

. The first consideration is of the concentration of new builds over the eight years leading up to the COVID-19 period. The new builds map has a sizeable hot spot concentrated in the Midlands, but there is no corresponding large cold spot. The vast majority of districts (257) fall within the NS non-clustering group (83%). The hot-spot districts have a median population density of 351; the cold spot (713) and the others (942) have higher densities. The Kruskal–Wallis test (KS), though, indicates that these are not different densities (χ² (2) = 1.476 [0.478]). Nevertheless, this does not point to new builds focussing on urban areas.

The national median rate of new builds/1000 dwellings is 6.44. This is duplicated by the NS group (6.21). The coefficients of variation (CoV) are also about the same: 0.443 vs. 0.431. The hot- and cold-spot new-build rates are also reported, as are the associated CoVs. The alterative Quartile Coefficients of Variation (QoV), which are more robust than CoV for ratios, present much the same picture.

One justification of a low district new-build rate is that the relevant district has a requirement to preserve a greenbelt. Using a Mann–Whitney (MW) test, the median rate within such areas of 5.87 is significantly below the rate of 7.25 found outside (−2.498 [0.012]). Of the 257-district NS group, 152 have some greenbelt land within their boundaries. The rate within such districts is lower than outside (5.85 vs. 7.2 MW = −2.736 [0.006]). This is not the case within the hot-spot group, where the building rates are higher (10.57 vs. 8.18), but this inference is not supported by a MW test (−1.95 [0.051]).

Table 1 reports conversions and change-of-use rates across clusters, again providing median rates for those with some greenbelt in their district. The inference from Mann–Whitney tests is that conversions and change-of-use rates are not different within greenbelt districts (−0.549 [0.583]; −0.601 [0.548]) compared with the outside. Again, the hot spots have higher medians, but these are not supported by MW tests. Nevertheless, using greenbelt restrictions as an explanation of a low build rate is complicated by whether the areas are classified as hot clusters or not.

Table 1 reports that the measures of spread for the hot and cold spots are narrower than for all districts in the case of conversions but broader in the case of change-of-use. Table 1 shows that, in general, the median, the CoV, and the QoV for the full sample and the NS group have around the same values. The hot cluster has a higher, and the cold a lower, median.

5.2. Assessment of Spatial Overlap

One expectation is that unaffordability drives new construction. The logic is that higher prices relative to income is signalling there is a shortage of property, and price would encourage house building [12]. As reported in

Table 2. Agreement and correlation pairs.

Dimension 1	Dimension 2	τ	κ	κNS	κHOT	κCOLD
	NewBuilds	0.121	−0.054	−0.138	−0.096	0.130
HPER	conversion	0.212	0.165	0.082	0.322	0.149
	Δ of Use	0.253	0.266	0.171	0.393	0.296
	LTVR *	−0.499	0.471	0.381	0.474	0.604
	demolition	0.187	0.048	−0.050	0.218	0.044
	conversion	0.013	0.081	0.060	0.077	0.131
New	Δ of Use	−0.007	−0.035	−0.062	−0.011	−0.008
Builds	LTVR	−0.135	0.051	−0.009	0.025	0.211
	demolition	0.089	0.004	0.007	−0.049	0.062
	Waiting list	−0.039	0.008	0.057	0.018	−0.092
	conversion	0.106	0.070	0.034	0.387	−0.086
	Δ of Use	0.018	0.063	0.060	0.248	−0.051
Waiting list	LTVR	0.065	−0.144	−0.186	−0.048	−0.162
	demolition	0.033	0.115	0.122	0.148	0.085
	conversion	−0.096	0.022	−0.043	0.172	−0.021
LTVR *	Δ of Use	−0.179	0.128	0.046	0.234	0.162
	demolition	−0.084	0.011	−0.053	0.063	0.068
Demolition	conversion	0.041	0.082	0.069	0.166	0.037
	Δ of Use	0.064	0.071	0.027	0.142	0.085
Conversion	Δ of Use	0.196	0.216	0.172	0.391	0.152

See Table 1 for coding, τ = Kendall’s correlation coefficient, κ = kappa coefficient, * the coding of Hot and Cold is reversed so that a cold spot should correspond with a hot spot of other variables.

, the non-spatial coefficient Tau indicates the correlation of HPERs at the lower quarter, and the rate of New Builds per 1000 dwellings is 0.121. Figure 2 displays the maps of hot and cold spots of New Builds, Change-of-Use, and Conversions. The agreement coefficient of −0.054 implies disagreement between new-build concentrations and those of affordability, but the value is not significant. The kappa coefficient of the larger territory of those that are not located in spatially distinctive areas (Random or Not Significant/NS) is not significant (κ_NS = −0.138), and neither is the level of hot-spot agreement (κ_HOT = −0.096). There is slight agreement over the locations of the cold spots (κ_CD = 0.130), but this is unlikely to be that informative, given the lack of a sizeable area where there is a paucity of new building. Combined with the relatively weak correlation, there is not much support for the hypothesis that clusters of affordability and clusters of new dwellings over the 8 years to COVID-19 overlap.

Conversions and Change-of-Use do not necessarily require additional land to be made available, so may be a preferred vehicle for district planners to add dwellings where building land is scarce. Using the English average rate as a benchmark, and generating a 2×2 grid of possibilities, a district authority could feature one type of addition at a rate above the benchmark when the other is below, viewed as using the forms as substitutes. For example, New Builds were added at a relatively low rate, but there was a high rate of Conversions of the existing real estate. Complements implies that New Builds and Conversions rates are either both above or below benchmark rates. If there was a general bias either for or against permitting additional dwellings across New Builds, Change-of-use, and Conversions, the intraclass correlation coefficient would be significant. As it is not (0.078 [0.208]), this suggests no global complementarity. Kappa, the coefficient of agreement amongst New builds, Change-of-Use, and Conversions, is 0.089. As well as for all districts, it assesses agreements among clusters of districts. The largest territory is that of those that are not located in a spatially distinctive area (Random or Not Sig/NS). That group also is found not to be complementary (κ_NS = 0.0571 [0.082]), whereas the hot spots (κ_HOT = 0.137) and cold spots (κ_CD = 0.097) point to poor agreement or weak global complementarity at best.

There may not be agreement among three components, but there could be among paired combinations of the three that disagree with the third. The philosophy behind Kendall’s tau is one of concordance: agreement in rank order over and above disagreements. Table 2 reports pairwise kappas with corresponding Kendall’s tau coefficients (using the rate data). The correlation between New Builds and Conversions is low (0.013), which is reflected in the agreement coefficient (0.081). New Builds do not align with Change-of-Use either. The negative sign implies disagreement, but the coefficient is not significant. Of the possible combinations amongst the three, the highest tau is between Conversions and Change-of-Use. Again, the kappa coefficient concurs. The overall agreement is most influenced by the hot-spot agreement (κ_HOT = 0.391 [0.00]), implying Conversions and Change-of-Use are complements in the districts that fall within the hot-spot clusters. This explains the weak complementarity finding above.

Change-of-Use is mostly office-to-residential, which is more likely to be found in urban districts. Both that and Conversions have small hot patches, more scattered than clustered. The median density of the population of districts classified using the Conversion data as hot spots is found to be relatively high, greater than for Change-of-Use (6624 vs. 2883), but the reverse within the cold-spot districts (413 vs. 528). The difference in the densities across both classifications is significant, at less than the 0.1% level. The hot spots for New Builds are in lower-density areas than the other two. Empty Homes [32] expected Leeds, Manchester, and Nottingham to have great scope for Change-of-Use. Of the three, only Nottingham ended up in a cluster, and that was a cold spot.

Figure 3 displays more dimensions of housing. Long-Term Vacancy rates (LTVR), Waiting Lists, and Demolitions have spatial autocorrelation coefficients of 0.533, 0.236, and 0.187. There is a prominent north-south schism in LTVRs, whereas Demolitions have hot spots in both regions. As such, agreement among them is likely to be poor. From Table 2, with the exception of Waiting List rates, the correlations with LTVR are negative. The degree of agreement between LTVR and other variables is weak. As suggested above, LTVR hot spots should be linked to low demand, and therefore likely to correspond with cold spots of New Builds. To address this, the LTVR coding for hot and cold is switched.

Following [18,19], demolition hot spots should be associated with districts with weak demand. A high LTVRs should collocate concentrations of neglected and structurally unsafe buildings which need to be demolished [20]. Only County Durham, Northumberland, and Sunderland are in a hot spot for Vacancies and Demolitions. Only Basingstoke and Deane and Westminster are in a hot spot of both Demolitions and New Builds. The Demolitions rate is higher in the greenbelts (0.32) compared with other districts (0.24), and this difference is significant (−2.373 [0.023]). The inference is that this is likely to reflect a restrictive land-use planning environment within a greenbelt, where reusing existing plots of land for residential purposes may be the only available building land. The kappa coefficients imply that there is no agreement in any category between Demolition and Vacancies, suggesting that the notion of an S-shaped supply curve discussed in [18] with a left tail is not supported.

When average vacancy rates are estimated for the clusters of New Builds, Conversions, and Change-of-Use, the categories present in a consistent order (Cold cluster vacancy rate > Random > Hot), and all are different at a level of significance of less than 1%. That is, vacancies are found at a higher rate where all three components of additional dwellings are relatively modest, consistent with a weak market thesis. Interestingly, the corresponding population densities run the other way (1060 > 642 > 573), where a lower rate of additions/high rate of vacancies are associated with more densely populated areas.

Amongst other housing pressure groups, Empty Homes, Shelter and Crisis are concerned about Waiting Lists and LTVR. The campaign group posits that areas with many vacancies are likely to be poor with high Waiting List rates, which can be brought down by bringing the vacant dwellings back into use. The discussion above implies that those likely to end up on a Waiting List for social housing will be housed in or around a city centre district. The Waiting List hot spots are concentrated in London, in the south of England, in Worksop in the midlands, and in Bury–Barnsely–Kirklees in the north. London, with the highest locational rent of all cities, has the longest lists. There is poor agreement between Waiting Lists and LTVR with or without recoding. If this is to be a policy link, the hot spots should overlap. The Waiting List hot-spot districts have a median population density of 7202, a level found in London only. Although city-focussed in numbers, the Waiting List clusters and groups have vacancy rates around the median (K-W 5.717 [0.057]).

One would have anticipated that, following [19], Waiting Lists would feature hot spots in Figure 3 covering larger cities in the north of England. Long-term vacancies are concentrated in the north of England. There is, though, a high level of agreement between the high affordability and high vacancy rates, consistent with the hypothesis of excess supply of housing in poor areas, which would imply more affordable rents, and would be in line with [19].

Although the accommodation may be less than ideal, were alternative means of adding housing found at high rates where there are long Waiting Lists? There is some agreement between Waiting Lists and Change-of-Use, at least in the correspondence between the hot spots of both (0.248). There is an even stronger agreement with Conversions (0.387) implying these alternative means of adding dwellings do follow demand in areas where there is a perponderance of poorer members of society seeking accommodation.

5.3. Structural Change

The data is split into before and after 2020, the year when much activity ceased due to COVID-19. The COVID-19 period led to a reduction in international migrants to London. There was a rise in home-working and a reduction in commuting, and so locational preferences, particularly around London, altered. Concurrently, there was a heightened rate of outmigration from London, particularly among 30–45-year-olds. The relocation was focussed on the Greater South East, with an emphasis on non-urban locations [41]. This remained the most popular destination for out-migrators across the two periods.

Another factor that could have instilled change is regulation. In September 2020, the Government widened what a PDR could be applied to, so that a further range of commercial buildings could be converted, and additional floors could be inserted into buildings that were for residential use [11]. That said, all new PDR conversions were required to afford adequate natural light to all habitable rooms, so this would have increased the costs and reduced the suitability of some conversions.

The rates at which dwellings were added per year post-2020 were higher than before. This is accounted for in the following way. The new-building rate increased (Sign Test coeff −5.98 [0.000]). With the PDR policy change, change-of-use was used at a lower rate (−4.973 [0.000]). There was also a reduction in conversions (−12.15 [0.000]).

The observation that outmigration from London to the Greater South East was persistent [41] is supported in Figure 4 and

Table 3. Agreement across pre- and post-COVID-19 clusters.

	τ	κ	κNS	κHOT	κCOLD
new builds	0.466	0.544	0.521	0.622	0.44
Δ of Use	0.373	0.372	0.348	0.357	0.423
conversion	0.406	0.351	0.319	0.695	0.076
Waiting list	0.549	0.627	0.606	0.796	0.568
LTVR	0.57	0.464	0.411	0.521	0.498
demolition	0.216	0.018	−0.010	0.010	0.072

. Tau and kappa point to a concentration of new builds in similar areas in the post-2020 period compared with before, particularly the hot spot. However, for both periods the spot is at the edge of the Greater South East. Conversions, which has a lower overall kappa value, has strikingly high agreement over the hot spot and no agreement over the location of the cold spots. The local authorities that authorized conversions in higher proportions were consistent over time. This echoes new builds. By contrast, the highest category agreement using change-of-use data is over the cold spot.

The three other dimensions of housing also paint a mixed picture. The median demolitions rate was lower (−7.15 [0.000]), whilst the vacancy rate was higher (−2.56 [0.01]) post-2020. Combining these two, the latter outweighs the former (−5.07 [0.000]). The results in Table 3 suggest vacancies have a persistent pattern, whereas demolition rates do not have such a relationship over time. It could be argued that the post-2020 period is characterised by [fair] agreement between clusters with a low demolition rate and high vacancy rate (0.21), so demolitions are better linked with vacancies post-2020 but not in the form of the S-supply curve [18].

Waiting lists have a high level of agreement across the two periods, particularly hot-spot districts. This is when waiting list rates were reduced (−3.13 [0.002]). London’s boroughs make up 14 of the 19 hot-spot districts.

6. Discussion

An observation in Table 2 and Table 3 is that the non-spatial coefficients tau or the intraclass coefficient align well with the corresponding kappa. Indeed, ignoring coefficients when LTVR is involved, the tau–kappa pairwise coefficients correlate at a rate of r = 0.9, suggesting there is some value in examining agreement between spatial autocorrelation classifications.

The large hot spot of new builds does not correspond with the relatively unaffordable areas or hubs with high waiting list rates. It does not fit with high-density centres. Gray [38] concludes that the pattern of child movement is indicative of that of 30–39-year-olds and a migration out of London to the Greater South East/South Midlands associated with forming a family unit, the first child, and house purchase. COVID-19 could have accelerated this established trend.

The two alterative buildings measures of change-of-use and existing residential property have weak overlap with new builds, suggesting they are focussed in different areas and thus alternatives for planners. Hot spots of both change-of-use and conversion have fair agreement. They can be viewed as substitutes for new builds and are complements to each other. Moreover, their hot spots correspond with those with high waiting list rates and HPERs. Where there is a concentration of long waiting lists or less affordable housing (the London area) there is relatively wider use of alternative means of adding dwellings. That said, both forms of conversion added dwellings at meagre rates (0.86, 0.12), way below that of new builds (6.44).

The post-2020 period is characterised by increased new-building rates with a drop in the offsetting demolitions rate. Change-of-use, conversions, and vacancy rates act as counterweights to this trend. Given the PDR policy change, this would be disappointing to policymakers, who would be looking for increased residential property in areas where conversions and change of demolitions are linked.

7. Conclusions

At its heart, this paper utilises a method of combining classifications of concentrations of district housing activity, as revealed by spatial autocorrelation. The classifications for each variable are assessed for coincidence with at least one other, using Fleiss’ agreement coefficient. It is found that there is a high correspondence between the coefficients of agreement, kappa, and the non-spatial measure of correlation, tau, estimated using the rates data. The similarity of values indicates that the agreement coefficients used in the manner presented have some use value. Kappa can be examined using a subset of cases (hot and cold spots), which policymakers may find useful. For example, finding weak agreement amongst two variables but strong agreement over areas of acute need focus the policy analysis. As a variant of correlation, the approach opens up the floor to further investigation behind the results of agreement between cluster footprints.

Hot spots in unaffordability and waiting lists data are taken as indicating market pressures in housing, which should influence mainstream and alternative means of adding to the dwellings’ stock. New builds are concentrated away from the HPER and waiting list hot spots, supporting the accusation that dwellings emerge in the wrong places, as some authors have claimed about planning and local construction track records closer to London [26,41]. The new builds are found to concentrate on the fringe of the Greater South East region. The concentration does fit the thesis that there is a migratory flow to the London market periphery by those seeking to buy and to start a family [38].

Reducing the flow of exits from the housing market is a means of bolstering the dwelling stock. Campaign groups, such as Empty Homes, Shelter and Crisis, seek to reduce the number of empty homes and the number of demolitions. Vacancies are found to be concentrated in northern regions, where housing is more affordable. Neither closely align with waiting lists. HPER aligns with vacancies, but only after the coding is adapted, the inference being that areas with less affordable housing have a lower LTVR. These tactics would increase the stock, but not in the places in most acute need. The demolitions hot spots do not correspond well with other variables’. This emphasis in the south of England, where HPERs are higher, does not point to a high demolitions rate necessarily being a symptom of a weak housing market. More likely, but needing further research, demolitions are a symptom of both a weak and strong housing market, the strong entailing the demolition of an existing building to clear what is brownfield land for the construction of a new one. Without knowing why a residential building is demolished, one cannot use the demolitions rate as a proxy for the state of the local housing market.

Change-of-use and conversion could be viewed as more sustainable means of adding dwelling spaces where green- or brownfield vacant sites are in short supply. Change-of-use is seen as a complement to conversion in that districts that use one at a relatively high rate are likely to use the other. Both appear as substitutes for new builds in that they are focussed in different areas. Despite recent successes, they have added dwellings at meagre rates, which declined after 2020. The permitted development right was hoped to boost repurposing commercial buildings for residential use [11]. The PDR policy alteration did not yield the desired outcomes and has been criticised for producing poor-quality dwellings. This does not bode well for the NPPF. Seeking to avoid the use of greenbelt by using more grey-belt land would imply an increased use of conversions. Indeed, change-of-use and conversion added dwellings at less than a sixth of the rate of new builds. They would have to increase their contribution rate by at least five to seven times for the new national targets to be met at the prevailing new-build rate. The two-period analysis suggests there is a declining role for these alternative means of adding dwellings.

As stated in Chapter 5 of the NPPF, delivering a sufficient supply of homes relies on a certain amount and variety of land coming forward. This includes greenbelt land surrounding cities (para. 67–68). Here, there is a strong emphasis on affordability regarding the release of such land for building. This points to the greenbelt around London as the best source of land to address housing pressures, reflecting known commuting/relocation patterns. Also, it is not clear that greenbelt districts have a lower additions rate. Although not statistically significant, greenbelt districts have a higher rate of new build than elsewhere. The greenbelt itself is not a surmountable restriction on additions.

The price of land can be a key problem for the provision of social housing. When public land is made available, its privatisation does not strongly feature affordable housing. Indeed, authorities with the greatest stock seem unwilling to use it directly to house the impecunious [7]. Perhaps a compulsory purchasing scheme, where the land is acquired by local authorities at a fair rather than an excessive price, who then build dwellings themselves, or where the private sector builds/converts real estate but there is shared ownership with the authority are ways forward.

The EIB point to devolution to lower-level authorities as being a solution in Europe [23] to a slow additions rate. Examples of working with planners to facilitate more and good-quality dwellings are presented [29,30,31]. In the UK, the light-touch free-market approach [29,30] is likely to produce volume, rather than quality, in places where builders can see a return. Even that volume is difficult to alter. Building practices and how land is made available would have to change radically to raise the new-build rate [24]. Indeed, even recognising the building industry’s management of the build-release rate, the CMA found that the number of permits was not sufficient to raise the additional dwellings rate to meet central government’s target [8]. When devolving responsibility for finding more housing land, local authorities in England were adept at restricting supply [5,6]. It could be that the current policy of setting mandatory targets at a local level will raise the number of dwellings added. But that is insufficient. From the European experiences, builders need better access to construction opportunities, and they need a stronger steer on what to do with those opportunities.

There are limitations in the analysis undertaken. The Getis–Ord Gi* reveals three clusters: not significant; cold; and hot. The not-significant group was by far the largest group/cluster, which means that the commentary was based on the minority of the districts. A nearest-neighbour or distance-based matrix could reveal larger hot and cold clusters. The matrices would not be affected by non-contiguity problems where islands are involved.

Fleiss’ kappas are best applied to variables with a positive association. The LTVRs are negatively correlated with most of the other variables. To account for this, there is a change in coding to avoid finding disagreement.

The waiting list is viewed here as a measure of the number of people in search of affordable rented accommodation. The list length was standardised by dividing it by the number of dwellings, in effect, by the whole population, not the renting population. Perhaps it would be better to divide the list number by the number of rented dwellings or possibly socially rented dwellings to get a sense of the likelihood of coming off the list.