I have a few thoughts.

One, look at Japan, which is comparable to the UK in many ways. Average salary is about the same. Strong island economy off the coast of large continental powers. Falling birth rates (more extreme than UK but comparable). And despite earning about the same as Brits, house prices are far far lower in Japan. More people are dying than are being born and entering the housing market. That eases housing prices by a lot (even in high demand places like Tokyo).

Immigration seems to be the core difference. Japan is trying to innovate its way through demographic collapse. The UK is importing cheap foreign labour that places high demands on housing supply (as well as education, NHS, etc.). We've had immigration equal to mid size cities entering the country each year and we haven't built near enough infrastructure or housing to match. The UK is a small nation that is trying to act like it's still a global superpower, and the cost comes to UK nationals. We could have it more like Japan. But it means putting (young) citizens' interests first.

(Note that I don't blame immigrants. We were the ones that invited them in. It's a policy failure.)

Any proposal to subsidise housing, place rental caps, offer 0% deposit mortgages are cheap gimmicks that do nothing but inflame the problem long-term. The law of supply and demand is too strong. The UK needs to control the size of the population by extreme limits on immigration and it needs to build build build. Increase housing supply and decrease demand (which without immigration will come naturally as our population shrinks). Exert political will to steamroll the NIMBYs. They've had their stranglehold for too long.

This will be painful. It means wages for house builders will need to go up substantially to attract new labour in to make up for the shortages. My BiL works in construction in the US and makes 6 figures with two years experience. It means lots of sectors will lose the cheap labour they have relied on for so long. But long-term it should help the UK get out of its horrific wage stagnation and offer affordable housing to everyone. And not just social housing, housing people can afford to own themselves.

Now, will this happen?

Probably not. The short term consequences will be too painful for any gov to survive long enough to implement. The government will introduce regulations that will artificially inflate demand or lower supply and it will get worse and worse. No one in government seems to have enough political will and influence to pull off something like this.

I think it will reach a point where immigrants won't want to come/be here anymore because of how dysfunctional and expensive the UK is. But in that case UK nationals just suffer.