Not only rich people. 8 people from my first university class did a year abroad on EU programs. (some couldn't afford it otherwise) At my last university, most of the year was not from the UK, which was funny when a GCHQ guy tried to recruit people - most of them not the right nationality to hire.

Or from another side, I expect most people from Poland are not going to work in the UK because they're rich and can afford it. They move where the work is and suddenly two parts of the family have a reason to travel internationally. Exactly because they're not rich.