According to the FT:
Transport for London is to build 10,000 homes across the capital during the next decade as it turns to property development to raise £1bn of funding for the capital’s underground system, trains and buses.
The group that runs London’s public transport network has shortlisted 75 sites, spanning 300 acres in total, to use for building homes, as well as office and retail space.
So public authorities can't build houses?
It seems they can if the funding is available.
And if it isn't there is People's Quantitative Easing.