That’s true, I didn’t mean getting in a prestigious university was rare from a state school, but rather those are certainly the “exceptional students” considering the stringent acceptance requirements. I only explained why rich parents would spend the money on private schools to give their child an edge. There are certainly cases where admissions are allowed because of family lineage or sizeable donations.

As far as I know you can only apply to Oxford or Cambridge, and furthermore you can’t apply to more than five universities in the UK except for rare occasions.