Not right now. Sadiq Khan seems completely comfortable talking about the housing crisis and not doing anything about it, and he's pretty much the only one who can.
If they announced (credibly) that they were going to build 75,000-150,000 new council housing units each year, house prices and rents would start to plunge.
If that were to happen they would have to be high rises and would be fought by the skyline campaign.
Sadiq Khan couldn't credibly announce that he was building 75,000-150,000 new council housing units each year because the money's just not there - that would cost tens of billions of pounds a year and his entire budget is only 11 billion (spent mostly on public transport and policing). It's also outside his area of responsibility; housing is handled by borough councils in London, and they don't have the money either.