Incorrect. The government build almost no social housing. They used to build 100,000 a year. They then sold it all off.
I am not the saviour, but building new housing can never be cast as part of the problem.
The real problem is that the government have deliberately made houses extremely difficult to build by adopting reems of archaic planning law, to stop new developments. The lack of supply of housing then makes house prices greater, so those with housing benefit, and stuffs everyone over who doesn’t have a house. I guessing this is what you are facing now.
The baby boom generation are the biggest beneficiary of this. My parents, two teachers, own over £1mn in property. My mum thinks she is one of the Candy brothers.