When it became quite (publicly) obvious that someone I know has some very wealthy parents . . . people took the (good-natured) piss out of them for that. Conversely, I've never come across people taking the mick if someone comes from a family that isn't well-off.
Even those (rare) people whose parents are subsidising them at uni above and beyond the level that student finance gives people will find that their friends don't have as much money, so it's not like they're all going off to mega-expensive bars, because if they tried that then they'd be going by themselves. Often, the only real way that you can identify such people is the fact that they can afford to drive a car despite not having a part-time job.
Being at the same uni is, in many ways, a great leveller. No one has large amounts of money, you don't know anyone, and they don't know anything about your background. It's a fresh start, and if you want (for instance) to go off and do something that is stereotypically considered to be "posh", then you can do it, because uni societies invariably manage to make these things affordable on a student budget - even flying lessons - and you'll find a cross-section of your own uni's population there.