OP, there are many other factors, too!
Wages have been consistently driven down in comparison to house prices and CoL. Who/what has driven this?
Greed: the greed of Companies like Thames Water, who have been paying out millions to their corrupt leaders executives and far too much to their greedy shareholders, while doing nothing to improve their service, in fact, letting standards decline so much that they release large quantities of raw sewage into our rivers and waterways regularly. At the same time, they reduce wages for the employees that actually do the work for them, while creating the maximum number of redundancies so that their operation runs at the lowest cost possible. This pattern has been repeated in every other industry, too.
In 1999, when I purchased the house I’m still living in, what I earned as a junior programmer, plus DH’s wages as an engineer, were enough for us to obtain a mortgage of 2.5x joint salary, we added that to the equity of £40,000 that had been growing since we became homeowners 15 years before, to buy this house. The mortgage we got was therefore, for just under 70% of the cost of the house.
26 years later, both me and DH have progressed in our careers, and are both at middle-management level - but what we are being paid now would not enable us to borrow any more than 32% of what the house is worth currently, if we use the same equation of 2.5x joint income - so it’s wage degradation in a huge part, too!
In order to rein it in, the Government would have to take action that would be unpalatable to landlords, newer home owners and investors in real estate, as they would have to set a maximum rental rate by area that was low enough to enable those on minimum wage to be able to rent on about 1/3 of their take-home pay…
Of course, if everyone could afford to rent at a much lower rate than mortgage payments on an owned property, home ownership would become less desirable, and prices would crash - eventually, and a new cycle of home ownership would be established. They would have to put a cap on ownership at that point, if not before, so that people with more money couldn’t buy more homes to make money from, and get us back to where we are now.
It would be wildly unpopular though, and take a very brave Government to do it!