Well, it may be a little different in the UK due to our many-tiered higher education system (Oxbridge, redbricks, ex-polytechnics and a moderate spectrum in between), but I'll chip in my two copper pence either way. Actually, this is a question I've thought about a little too much, I'd wager, because, as a prospective undergraduate, I actually turned down an offer to read mathematics at Cambridge and decided to study…
1. Did you go to public school? (i.e. privately educated) 2. Was either of your parents a doctor?
If you answered either of those with 'no', then the concensus was you could kiss that place goodbye.