I went to what is usually referred to as a bog standard comprehensive. Not a grammar, and definitely not one of those comprehensives that's in such a posh area that it might as well be selective.
I got straight As in my A-levels. In addition, I got the highest grades in the country in two of them (yes, exam boards do write to the top five in each subject). I also got the top grade in all my three S-levels. I was made to sit these and to apply for Cambridge by my school, for whom it was a PR coup, as no-one from there ever went to Oxbridge. They even called the local paper when I got in. I did the exam entry, not the interview (which I would instantly have failed, to this day I remain the world's crappest person at looking clever when I am talking).
The reason I'm mentioning this is not to boast, but because there are so many people on this thread who are insisting that if you are able, you will definitely apply to Oxbridge and that anyone who doesn't is just likely to fail and probably isn't able to get in. I just wanted to say that this is bollocks, and that you can be bright and be happy and do well elsewhere.
I ended up going to Cambridge for about 10 days on a scholarship place that I had very much earned and I HATED it and dropped out. One thing I just don't encounter in these discussions is any sense of how utterly lost you are as a working class person in this new world. I was completely unused to all of the social rituals. I turned up in inappropriate clothing which was laughed at, and I didn't know how to deal with things like being waited on because I'd never even been to a restaurant before except McDonalds once or twice for a really, really special treat. Because of the money, I was singled out in terms of my accommodation and also asked to go and talk to certain academics. Where I grew up, you don't talk about anything clever because 'you might make a fool of yourself'. I was terrified of looking like an idiot and started to be sick before each of these "introductions".
I was scared of the other students, too. I had never met people before who boasted all the time about what they'd done - my whole education had been about hiding the fact that I was bright because otherwise I got mercilessly bullied. The 'other kids from state schools' who I'd been assured would be there didn't seem to be from the same kind of background at all, but were largely from posh grammars that had things like sports facilities and debating societies and uniforms. I had never before dealt with people who just flat out told you you were wrong with utter assurance, or who never asked you what you might think or feel! Hell, I'd never even met people with plummy English accents before.
I ended up leaving and going to a Russell Group university where I was much, much happier. It wasn't like it felt normal - perhaps I had been broken in a bit by the experience of being so alien? - but it didn't feel so painful either. An older academic took pity on me, and took me under his wing. He found me a place at his uni, and later supervised my MA, helped me get into a top PhD school, and wrote references for my first academic jobs.
I don't know whether pulling out of Oxbridge was a good choice or not. In retrospect, if I'd stayed, I would have been forced to acquire those skills that are essential to survival in middle class life, which I still don't really possess. I'd also have got the right network on a plate, which (let's be honest) is why most of their graduates succeed - it's all about knowing the right people and having an 'in'. But there was such a howling chasm between the world I knew and the world I encountered, and it generated massive anxiety.
So I say to all those who don't like the idea of it - go, have a look round, and make your own judgement. You might not find it nearly as bad as I've painted. But if you don't feel it's right for you, you can be happy and successful elsewhere too.