But unless wages keep up with house prices (and therefore what you need to borrow to get one), you cannot raise interest rates much without financially destroying most people.
House prices have gone silly, but then causing a housing crash will also trash the economy as well.
The mismanagement of the economy has pretty much cornered us.
We have already surpassed the 1980/1990 peaks in terms of relative affordability. The bank has no more room to act without crashing everything, and their ability to use interest rates becomes less and less workable as house prices continue to grow.
It's not just about house prices. If you don't increase rates then the currency will lose value increasing the cost of everything. People need energy, cars, food etc etc.
I completely get that it's a shock for people with mortgages going from a low fix to current rates and potentially even higher in the future. The house market is unlikely to crash significantly but will probably stay stagnant for a few years whilst inflation eats away at the size of the debt and rising wages bring affordability back in line with historic norms.
As it stands most homes are owned outright anyway. The government will probably have to build some social housing over the next few years to help young people and create some social mobility. Availability is a problem in the rental market.
What we can't do is keep rates low to sustain the few that have large mortgage debt at the expense of making everything else more expensive. This isn't just a UK problem as low interest rates have caused housing price growth everywhere. We are probably in a better place to weather the storm as so much of our property is owned outright. Economies which have more housing debt are in a worse position.