Everyone quotes Oxbridge, UCL, LSE and Warwick but ultimately I find that it is how hard you want it more than anything. Perhaps I am saying this because I'm not going to the aforementioned universities in September but I have seen people from Edinburgh, Royal Holloway, Bristol and Birmingham get into investment banks and have never heard of Oxbridge graduates getting into IB. Obviously it's because I don't run with that crowd, but I think by virtue of the people from a wide array of universities and disciplines getting into IB, I would say that the statistics that "80-90% of graduates in IB come from those top schools" is a load of rubbish. Rubbish, perpetuated by people on the board and propagated by hear'say throughout the years. Obviously the more prestigious school you go to, the better, but don't write yourself off if you don't.
This isn't a reflection of everyone, but a friend of mine went to Royal Holloway, got a 2.1 in economics, no previous experience, worked in Budgens and now got a job at Barcap. How did he get it? He just tried really hard.