Builders are not fools, they build the type of house they know they can sell. In many prosperous areas of the south east a lot of people can afford detached 4 bedroomed houses. It may be their second or third house move so they have plenty of equity.
We used to live in area with a much higher than average number of people working in research of all kinds and high tech companies where highly skilled staff were paid salaries to match. A couple, both in high tech jobs are probably earning at least £50k each, which is a household income of £100k. They can afford a 4 bedroomed detached house.
I know, I know that there are vast numbers of people who do not earn those kinds of salaries but there are a lot who can. Housebuilding companies are commercial companies, they need to make a profit and they need to sell properties quickly. They are not charities or social enterprises.
If the government wants more smaller properties on accessible sites, which might well be loss making if built by a commercial property, then it just has to fund social housebuilding itself.
Before Mrs Thatcher, a third of all households lived in council houses. These were built because it was the only way that people on lower wages could access decent housing. On the commercial market they could only afford to rent slums. Let us get back to that. These houses gave security of tenure to those whose lives were often on a knife edge for money and work.