From what I've heard, there's a very different atmosphere in Private Schools. I guess because kids are aware their parents have paid for them to be there, there's a bigger incentive for them to work hard, so it's more of a social norm to complete your work to the best of your ability. As opposed to a lot of state schools (not all) where there are students who just don't want to be there, a lot of whom are under a lot less pressure from their parents, and if there's a large enough number of them, they create an atmosphere where it's "geeky" and "uncool" to give homework in or show up on time for class.
Plus the standard of teaching is going to be very different, as I'm assuming the jobs at under-achieving state schools will be a lot less competitive than those at the top private schools, and these lesser-quality teachers often have to deal with much more difficult students. I think an average of 60% of each lesson I went to was spent listening to a teacher try and get students to stop throwing books at each other...etc.
It's definitely still possible to achieve highly. I still managed to come away with 7 A*s and 6 As, but I was one of very few. And whilst contextual information is taken into account by universities (which I for one am very grateful for), I can't help but feel that the 3 As I'm on target for at A2 might have been higher had I not had to deal with so many examples of bad teaching during my time at college. I'm not blaming the teachers, as I'm sure there'll be students at my college who come away with A*s so it's entirely down to how hard-working and intelligent the individual is, but I feel like you perhaps have to be slightly less hard-working at a school where you're not trying to teach yourself the majority of the material. (Not that I'm putting down people with good grades from private schools, I just think they're harder to get at state schools).
As for fairness, it isn't really. I don't think money should have an impact on a child's right to decent education, which is why I am a little uncomfortable with the idea of private schools. I think grammar schools are a good idea - separating those who are capable of achieving highly from those who aren't, rather than those who are capable of paying from those who aren't.
Anyway, I'm sure there are some advantages of going to state schools if you don't focus entirely on the grades - I think it's made me a lot more independent than I would have been if I hadn't had some of the awful teachers I've had.