I think there is something else which also impacts the reluctance to build massive numbers of affordable houses.Primarily a planning problem when you compare us with other countries
Four million UK homes missing due to outdated planning laws - Centre for Cities
Compared to other European countries, Britain has a backlog of millions of homes that are missing from the housing market. Building these homes is key to solving the nation's housing crisis.www.centreforcities.org
Any government which builds at the rate required to house the population at costs people can afford would need to create an over abundance of housing. This would for certain reduce the average price of a house and reduce rents. Where there is a surplus of housing, prices are much lower. It is caused by basic economics. Here's the thing that all politicans facing this problem know. VOTERS would NEVER forgive any party which caused their prize asset to decline in value. Therefore - NO government will do it.
Long ago - elsewhere I was writing that government should never have invested all the vast money they did in a railway line between London and Birmingham. I can't even remember how many billions has been spent on that massive white elephant. ALL of that money should have been spent on a Macmillan style massive house building boom. Not big expensive villas, but nicely built, sensibly priced houses for sale and rent. The rental part of the portfolio ought to be bound up in trusts that mean they can NEVER EVER be sold off into the owner occupier market as happened to the ex-council houses. The so called right to buy should be repealed.
Doing as I have said here would have transformed the lives of the young.