The UK is one state (still, just) but four countries. The US is one country with 50 subsidiary states. The structure is just different. I don’t think there’s a lot of point comparing them in this discussion. Social class structures and mobility are more complex than anyone here seems to acknowledge.
Purple Titan, I think the student’s school background is considered as part of the picture, for domestic applicants. Here’s an article in which the head of admissions at Oxford says as much here: http://www.telegraph.co.uk/education/educationnews/12089249/Children-need-to-be-coached-for-Oxbridge-from-age-11-says-head-of-admissions.html