As a libertarian, my default position is to assume that the state makes problems worse. So, in the case of housing, my remedy would involve the state getting out of the housing business. This is not based on callousness, but rather a genuine belief that the free market is far more capable of handling the allocation of scarce resources than any system of bureaucratic management. Furthermore, I see the distinction between "social housing" and other forms of housing as essentially spurious. Everyone needs a home, after all. By rejecting the free market, we are confronted with the problem Ludwig von Mises identified with regard to socialism, namely the impossibility of economic calculation, once the market approach is abandoned. It is no longer a matter of what any particular person can afford, but rather an amorphous "need" that has no effective limit. The same thing applies even more so with regard to healthcare.
There are no easy solutions to such a major issue. As ever with economic matters, sooner or later we must consider the elephant of the monetary system, and all the harm and distortions that causes. When the subject of inflation is discussed, rather than the original definition of inflation as an expansion of the money supply, what is meant is the increase in prices. The official measure of this is based on an arbitrary selection of goods and services, which does not included the cost of housing. We have often been encouraged to view the steep rise in the price of housing as a good thing, at the same time as being taught that a similar rise in other prices is bad. The cost of housing has risen in part due to a shortage of supply and in part due to the artificially low interest rates, thanks to the central bank interfering with the market.
Another matter concerns land ownership. Although we often hear that Britain is overcrowded, in reality the population is crammed into a small amount of the land mass, with vast tracts remaining undeveloped. When we look at the ownership of the land, we might almost be reading from the Doomsday Book! It is, however, somewhat late to seek redress for the expropriation of land at the time of the Norman Conquest.
Then there's the issue of planning laws and nimbyism ... but that's enough thinking for now, my brain's beginning to ache.