For new housing the problem is that landowners and developers do not factor affordable housing (or rent controls if applied) to the purchase price of the land. As such, when they apply for planning permission they say, sorry gov, no money left for that. Look what happened to elephant and Castle.
The problem is that most in power (except BoJo?) will not take risk of saying, it's now unaffordable buy a house let's build rented properties. The big housebuilders are actually very pro building rented properties and quite anti starter homes being classed as affordable because they can see that there is a hugely bigger market for rented properties in London.