That sounds suspiciously like a political way of blaming some other group that no voter will be a member of so it's pretty safe for politicians.
The fundamental problem is not enough houses, not that UK people aren't xenophobic enough. Just allow developers to build more and prices will come down.
No that's not it at all. The fundamental problem is that everyone wants to live in the same few square miles of London, exacerbated by the fact that London property is seen as the new Swiss bank account by ultra-rich foreign investors from let us say less than stable regimes that might simply annex their wealth one day.
The fundamental problem is not enough houses, not that UK people aren't xenophobic enough. Just allow developers to build more and prices will come down.