I mentioned tax breaks, or 100% forgiven tax on selected building projects, but only with agreement as to maximum sales and rental prices. Add council house building with no possibility of sale, and that's more cheap rents.
These cheap houses would force other rentals down because buy to let landlords would have no choice, and they'd probably go under bit by bit. That means even more downward pressure on house prices as they sold up. The only thing the tories could moan about is estate agents and greedy landlords that made the housing market go mad losing their businesses, and who likes that bunch?
The tories would be arguing for high rent and house prices, so shooting themselves in the foot. They aren't that idiotic as to complain, and involving private builders means they can't moan about projects and public without saying capitalism is bad and .. err, what public spending?
They could moan on about lost tax revenue, but tax that would never have been taken isn't lost.
However, the goal of cheap housing is realised.