@LondonJJ - there's exceptions to that - the obvious is the number of people who did PPE at Oxford who end up in the Cabinet, though it's not the whole story as half of them knew each other beforehand; also the contacts made via Cambridge Footlights, or various science labs (not that there aren't great science labs in many places, but the Golden Triangle of Oxbridge+London is an excellent incubator of science talent).
Someone said upthread that if Oxbridge toned down the emphasis on traditions, it would be the same as any other uni - hardly. The THE ranking of world unis has Oxford and Cambridge invariably in the top five (1 and 3 this year here - Imperial and UCL also make the top 20.
I've done a bit of work in getting kids from non-uni backgrounds to apply to good unis (not necessarily Oxbridge, but trying to get them to consider it and reject it based on facts not hearsay). The fact that rent is cheaper than most places should be advertised more, along with the fact that there are less ancient colleges which don't do the dinner thing or even have oak-panelled halls, that there are lots of book grants and bursaries and hardship funds and it's much easier to get a good job for the summer if you can work 13 weeks rather than 10. And you won't even need to pay for a bus/train pass to get to lectures or to go out of an evening.
Also explaining that yes, there are balls that cost £250 for a night, but the people who pay are mainly either thrid-years doing it as a one-off, or alumni doing it for nostalgia, and that the vast majority of epople attending get in by doing work for the event (before, during or after) and getting a discount or free ticket.
And that yes, rich people exist, gobby rich people exist, but if you've got in you've got just as much right to be there as anyone (and rich people get as insecure about their achievements as anyone else).
Apart from the ones who were certain they wanted to do particular courses, reasons for rejection included 'I want to be in a big city' (usually from London/Birmingham, usually wanting certain types of music club night - some liked the idea of it being easy to set up their own nightclub event), lack of options for a year in industry (true, though in many fields a summer placement and feeding into a final year project is just as good), 'it's too far south/north/east', and wanting to stay at home (or parents wanting them to). 'Too many white people' was one way some would express discomfort with it being not-London, and yes, a mainly-white uni is a huge contrast to Southall or Peckham or Walthamstow, but I was shocked how many of them thought that all of Britain had a similar ethnic mix to London and it must be racism that meant you didn't see BME students or people on telly so much.
One side-effect of higher degrees becoming more common is that students are often more ambitious second time round - bit like in the US where many people go to their local community college for two years, then if they do well, are brave enough and willing to pay for a more prestigious college.
I've just had to choose a secondary for ds, state as he couldn't cope with an exam despite being bright, and got to compare the contenders with a couple top public schools. The facilities are remarkably similar; the difference is more teachers at the privates, and some extra academic subjects (but no BTECs etc). And large dedicated inclusion teams at the comps. Will have to see how it pans out - ask me in five years time...