Two young people I know (but unconnected with each other) who had offers from Cambridge both turned their offers down. In both cases they had decided that they preferred the structure and content of the course (Maths in one case, Psychology in the other) on offer at Surrey, one of the UK’s newer universities. Both have gone on to do doctorates, and have done well, and neither regrets their choice.
I think a certain amount of “it’s ancient so it must be the best” snobbery attaches itself to Oxford and Cambridge — either that or “it’s quite new so it must be rubbish.” In 1970, my best friend and I were very attracted by the new university of Warwick. Our elderly English teacher pulled herself up to her full 4′ 11″ and remarked, “Well, if you wish to apply to a jumped up polytechnic, that is no-one’s concern but your own. However, you will not cite me for a reference!”
It is statistically harder to get into Warwick to do English than Oxford.