No, it would BE BOUGHT by government at fair price (they know the fair price, just look your houses tax bill)
Or built by them.
And then rented out with a certain maximum rental price per Sq Mt like 10$ so 50sq m (500sq ft) = 500$/month
Most importantly, they would be obliged to make it Energy efficient by their contract with the state so much lower electric and heating bill, maybe even topped off with solar, would be small percentage of a new building but cut costs for actual people.
Not saying it's perfect in Holland (they have shortages because no new land available to build new social housing projects), but it sure works!
Thatchers plan would have worked if and only when:
LAND IS PROVIDED FOR NEW PROJECTS (destination plan on national provincial and local level)
ALL INCOME FROM RENT TO BUY (or similar) IS SPEND ON NEW PROJECTS
ALL PROJECTS ARE GUARANTEED BY THE BUILDER (no excess costs for any reason : sign your profitable contract but then you are obliged to deliver exactly what is promised or you'll never get another gov project again)