Not everyone agrees there's a shortage:
https://www.theguardian.com/lifeandstyle/2024/mar/19/end-of-...A few choice paras (if people don't read the full article):
"The forthcoming general election is once again likely to be dominated by claims about a housing shortage and a dire need to build more homes. Housebuilding is an article of faith across the political spectrum. The evidence, however, does not support this thinking. Quite the reverse. Over the last 25 years, there has not just been a constant surplus of homes per household, but the ratio has been modestly growing while our living situations have been getting so much worse. In London, as the Conservative Home blog notes, there is a terrible housing crisis “even though its population is roughly the same as it was 70 years ago”, when the city was still extensively bomb-damaged by the second world war."
"The supply issue continues to dominate the discourse despite the US having more homes per capita than at any point in its history, and the UK’s homes-per-capita ratio actually exceeds the US’s."
"In terms of the Organisation for Economic Co-operation and Development countries, the UK has roughly the average number of homes per capita: 468 per 1,000 people in 2019. We have a comparable amount of housing to the Netherlands, Hungary or Canada, and our housing stock far exceeds many more affordable places such as Poland, Slovenia and the Czech Republic."