I think you might be missing cultural differences here.
I can't speak for the UK but here in Germany people usually don't just "buy a house" in their 20s, because of the debt involved (guess we are very opposed to debt). In my experience that would happen only at least 10 years later, when you have saved up a sizable down payment. Also selling a house again is a really big deal, kinda rare. There's not a lot of switching, like I hear from some US friends.
So yes, this has nothing to do with support from your parents or general income/wealth bracket. If you are standing on your own feet, you move out to a cheap apartment, often for the first time with your partner. Also please remember that we have a lot less campus universities, people usually live in a small apartment in the city they are studying in (same with vocational training) and not on campus.
(Please correct me if you don't think that a sizable portion of people in the US buy a house before they are 30, no matter if they are "filthy rich" or just working a normal job)
And now for a completely made up theory: If you're going into debt for your degree maybe you don't care as much to get into more debt if you move into a house when starting a job, because you're already in debt. But if you got through uni without getting into debt, either you don't want to do that, or (more likely) you wouldn't even get a loan from the bank here, if you never worked before.