This is silly. 44% of the English population lives in Greater London or the Southeast. If I could get figures based on age, I would imagine that the figure for genY and millenials would be even greater. It's not a "niche" concern.
How are these kids going to pay off their student loans? Remember with 50% going to university, they now have to go to uni, and pay for it, to the get same jobs people managed with just A-levels, or even just O-levels in the past. So of course, they have to go to where the jobs are. Good jobs and cheap housing are inversely related.
As for inflation, it's very tough when your variable rate mortgage shoots up. But historically, when inflation jogs, so do wages. They lag a bit, so it feels tough, but they do follow. And, inflation eats away at the real value of your mortgage. High interest rates are a transfer of value from creditors to debtors. So, I think it is very hard to argue that as a group, baby boomers did not benefit from the macroeconomic conditions at the time of life when most of them were taking on debt (mortgages.)
Additionally, 5% mortgages are hard to find these days and if you do the interest rate is relatively punitive.
If millenials are moaning about the system being unfair to them, well, they are right. Frankly, the system has neither been designed nor tweaked with their interests in mind. Of course, the best way to change that, is for them to become more politically engaged and to vote more often.