I'm not sure the 'housing shortage' that we are continually being fed is as real as some would have.
When we got married in 1968 our new house was £4,250 being a 10% deposit (I think) and a mortgage 3 times my salary. That was all that was allowed.
A few years later the government removed that constraint, so many people took out mortgages far greater than 3 times their salary. That brought about gazumping and the consequent rapid inflation of house prices.
I don't think it was ever a 'legal constraint', more like a 'best practice' kind of thing. When I bought my first house in 1998, the guidance was still 3x salary, or 2.5x joint salary. When I bought my second house in 2008, we were again only allowed 2.5x joint salary, and only just managed to scrape a mortgage or £125,000. It was a 100% mortgage, so we got stung with a massive interest rate for the first 5 years (more than we're paying at the moment).