From the 1970s–1980s, UK government local authorities stopped building homes:
(Source: BBC News)
Or, with raw figures from the Ministry of Housing, Communities & Local Government spreadsheet, extracting figures for England and Scotland for completed council homes in selected years:
England Scotland 1970 130,180 34,660 1975 116,330 23,190 1980 74,840 7,490 1985 23,310 2,830 1990 12,960 1,630 1995 760 720 2000 180 110 2005 300 0 2010 1,140 610 2015 1,900 1,140
Why did UK local authorities stop building homes since the 1980s?
Although houses were built by local councils, funding came from the central government so the political decision to no longer do so was taken in Westminster. So the direct answer would be because they cannot afford to, but what motivated the political decisions stripping councils of money to build homes?
Although there's been some recovery in the past 15 years, building 2,000 council homes per year is far below demand. Scotland does a little better, it has 1/10th of the population that England does — per capita, Scotland has usually built more council homes, and are now building around a factor 5 more. Scotland does not have the right to buy, and has had more progressive governments than the UK (which decides for England), so either the right to buy and/or the more progressive governments may be part of the answer to the lack of council house building in England. I'm not sure how the right to buy would lead to lack of council house building; one might equally reason that the privatisation of council houses through the right to buy should necessitate a steady construction of new council homes.
Background reading: Tom de Castella, Why can't the UK build 240,000 houses per year?, in: BBC Magazine, 13 January 2015.