I went to a super selective all girls private school in central London around 20 years ago. Most parents were doctors or lawyers, but there was a lot of parents from many different backgrounds too. It was a pretty low key experience all in all. Obviously there were some super rich kids there, but I'd say the vast majority weren't. The thing that stands out now from reading these boards, is how intense the private school experience is now.
Multiple music lessons, sports teams on Saturdays, super intense homework session. Non of this really happened when I went. Again, obviously kids worked hard etc, but it sounds so much more pressurised and these days