House prices aren't that tightly linked to incomes. House prices are more strongly influenced by interest rates and availability of credit. And, of course, supply/demand fundamentals (ie: population change vs. number of housing units in an area).
I believe banks in the UK don't lend you more than 4.5x - 5.5x of your income, regardless of interest rates.
As a result 5x and 6x income mortgages tend to be easier to get the more you earn.
If I was, then I'd say a system where the government basically gives you free money/tax breaks if you buy a home, is the root cause behind the things you mentioned which then drives house prices.
The point is, without fixing that issue, you can't solve it by wage rises.
People who don't even want homes are buying them, either as outright investments that they can sit on for years, or as something they also live in, but need to treat as an investment, rather than a home.
Such as? MIRAS was abolished 20 years ago. Homes are arguably under-taxed (no US style property tax), but that's not really a "break".