The Resolution Foundation points out that people are spending three times as much of their incomes on housing today than they were 50 years ago, and that 30-year-olds spend more of their income on housing than did their grandparents at the same age.
You can see this as an inter-generational injustice. But there's another question here: are high house prices bad for the economy generally? I suspect they might be, for several reasons:
First, sharply rising house prices are associated with increasing household debt, which increases the chance of a financial crisis which has long-lasting adverse effects upon growth. As Mian, Sufi and Verner conclude (pdf):
An increase in the household debt to GDP ratio predicts a subsequent reversal in debt and lower subsequent GDP growth. The predictive power is large in magnitude and robust across time and space.
Secondly, housing is prone to the Baumol disease. Because the housing sector has lower productivity growth than other sectors, a shift in spending towards it tends to reduce overall productivity growth. To put this another way, if younger people weren't spending so much on rent, they could spend more on other things, which would stimulate output, innovation and entrepreneurship in more dynamic sectors.
Thirdly, years of rising house prices have encouraged a culture of investment in bricks and mortar. This has diverted potential entrepreneurs into "property development" and away from perhaps more socially useful activity; has encouraged people to regard their house as their pension and so diverted capital away from business investment and formation; and might have encouraged early retirement and a loss of skilled labour*.
Fourthly, high house prices give people an incentive to protect their investments, and this breeds the sort of nimbyism which can delay infrastructure investment.
Fifthly, high housing costs encourage people to commute long distances. Not only is this bad for their well-being, but it can also depress their productivity.
I'll grant that there are some offsetting considerations. In the past, high house prices have been a source of collateral for entrepreneurs; thousands of people have taken out second mortgages to start businesses they'd otherwise be unable to. However, with so many energetic young people now locked out of home ownership, high house prices are perhaps less likely to stimulate entrepreneurship in the future.
Also, you might argue that it's not wholly a bad thing that people are forced to rent. Andrew Oswald has shown that high home ownership impedes labour mobility and so raises frictional unemployment. I'm not sure how relevant this is, though. Big differences in rental costs across the country can also reduce mobility: many people can't afford to move to London, even if they were stupid enough to want to.
My point here is that we shouldn't simply be asking whether high housing costs are an unjust burden on young people. We should also consider the possibility that they damage the whole country's economic prospects. Slower long-term growth means there'll be less to spend on (among other things) the NHS, so even those of us who have benefited from high house prices up to now might suffer in future. Torsten Bell might well therefore be right to speak of a "housing disaster".
* I'll be retiring early thanks to the house price boom of 1994-2008 - not that it'll be a loss.