s/rent control/more housing/ and then yes.

Or perhaps do both, even better use housing vouchers instead. But you'll never rent control your way to a functional, affordable city. It can be a better bandaid than doing nothing at all but it's too untargeted and has too many downsides. And it very much falls into that same trap of thinking that young people aren't real residents who also need housing.

Local council budgets are strangled enough as it is, and social housing is quite costly.

This sort of scale has to be driven at government level and the tories have a vested interest in keeping house prices as high as possible so that their voter base sees a return on their investment.

Also, “luxury” is just a nimby boogeyman and doesn’t mean anything. Older housing is still very expensive, because there is simply not enough housing. Even if new housing does come with a small premium over older, people move out of older housing into the newer housing freeing up space in the slightly less expensive older units for lower income residents, and the market as a whole gets less expensive as you build enough housing to meet demand.