The answer to all of this is deeply unpleasant for those people who own their own homes - but it is that there needs to be a national target for a maximum house price to income ratio of 4:1 or maybe, at a push, 5:1. That means house prices need to not only stop growing quite so fast, they actually need to fall dramatically. Anyone who owns their own home is obviously going to hate that. But the sad fact is that the market is broken and needs radical action to fix it.
I can understand why the public's immediate emotional response would be to reject this.
BUT if mortgage balances were also reduced downwards so that no one ended up in negative equity, it would benefit most people.
If you sold your current house you could still buy an equivalent house elsewhere with no loss of money.
If you were upsizing it would cost you less to upsize.
If you were downsizing or emigrating you would, however, get less back.
Everyone would pay off their mortgage much quicker and be able to spend their money on more interesting things.
Even if you're worried about what you'll leave your kids, your kids will still be in an equivalent financial position (unless they've already paid off their mortgage in full). They need a house each, and each of your two kids have inherited half a house in value. They can then go and put down a 50% deposit on a mortgage on an equivalent property (or pay off the mortgage). It doesn't matter if the sums involved are £50,000 or £500,000, it's still half a house.
Of course your proposal of a maximum price for houses linked to income would need to be much more nuanced to account for huge London mansions skewing what happens to 3 bed semis, but overall people wouldn't lose out as much as they imagine in the event of house prices falling IF mortgage balances were adjusted downwards and no one ended up in negative equity.