For anyone doubting Rubbles statement, house prices haven't been rising over the last few years everywhere in the country. Prices have been falling or flat where I am for years (Yorkshire)
We last bought in 2006 and the house was probably worth less than the price we paid until a couple of years ago at least, but prices do seem to have risen over the past year or two. Luckily we had equity from a previous house but anyone buying without a deposit at that time, where mortgages of up to 125% were available, could still be in negative equity, or not have much equity.
If someone had bought a house like ours in 2006 for £120k with a £150k mortgage, the house will now be worth £130k at most and I CBA to work out what their outstanding mortgage would be, but it will probably be about £110/120k.
If prices for houses like mine fell to £100k, which is what they were about 5 years ago, they wouldn't be able to move without paying out ££££s, which they are unlikely to be able to do. So there would be less houses available to buy too.
One of my other fears about Brexit is that we will start to lose a lot of the employment rights that being in the EU has given us. if more people have unstable employment, because we know what our government thinks of people who have to work for a living, it will be much harder to get mortgages anyway.