"Even with low interest rates, house prices have been ridiculously hugh compared to wages."
You've kind of missed the point. Low interest rates mean people can borrow more. Which forces up house prices because you have more money chasing the same thing.
People falling over themselves to borrow more money, bidding prices against each other, while the banks rub their hands.
Now people who didn't subscribe to this sort of madness are in a good position, people who did are crying "it's not fair".
The government doesn't control monetary policy (interest rate), the BOE does. And the BOE is supposed to be independent of policy. But it's policy is largely influenced by the worlds other large economies. In particular, the US interest rate set by the Fed. If you look around the world interest rates are rising everywhere. Europe. Australia. US. They all follow in together. They have to otherwise all the money will flow to the country who sets the highest rate (return on money). There are some other mitigating factors (for example risk of return) but generally this is what drives interest rate policy outside the US.
What people can blame the government for is not applying specific policy to housing to cool the market down. Examples of this might be placing minimum loan to values, lower maximum earnings multiples and higher stamp duty.
Instead the government have done exactly the opposite, pumping the market year on year to try to get popular support. This has been done since at least 1997, so encompasses both Tory and Labour governments. I think even recently some bank stress testing for mortgage holders has been relaxed. Absolute madness when what we need is higher levels of stress testing.
At some point the music stops. We've now hit a double squeeze, mortgage rates rising at the same time the cost of living is rocketing (these are to some degree related, but not completely).
The fall out is going to be epic, unless the Fed decides to roll back on interest rate rises. There are some rumblings that this may happen, and they are starting to come under some external pressure.
We'll see what happens.