I call bull on that. As the first country to industrialize, and arguably the first to de-industrialize too, Britain has massive amounts of brownfield ready to be used.
The problem is just that developers have to pay to clean up those sites. You can simply look at the Houchen affair: as soon as the local authority foots the bill, developers will jump on the dirtiest stretch of brownfield, no questions asked.
i.e. more cost, which gets passed onto buyers/renters. Different entry point, same result. Plenty of brownfield sites do get redeveloped, particularly in city centers, but they don’t become affordable housing, they become trendy apartments with industrial heritage museums next door (and not enough of them).
The population of Britain has increased nearly +10M in the 21st century, but the housing supply has lagged far, far behind.
I'm not denying there is a supply problem, what I don't agree with this that it'd be because of some silly obsession with protecting greenbelts. Protecting greenbelts is important, and there are alternative policies that can incentivize house-building without losing more green spaces.
If there is one British obsession, is the expectation that every family should aspire to a semi-detached in the suburbs, with the result that (outside of London) developers only build small flats for singles and childless couples. The semi-detached model does not scale, while flats do. Developers should be forced to include larger flats in new builds, and councils should start thinking in terms of making town centres denser and more attractive to families.
The problem is just that developers have to pay to clean up those sites. You can simply look at the Houchen affair: as soon as the local authority foots the bill, developers will jump on the dirtiest stretch of brownfield, no questions asked.