Just adding my two cents to the whole prestige argument here.
I don't disagree at all with the argument that KCL gives you more career opportunities than say, Exeter or York. However, firms want a lot more from graduates than purely a good degree. You have to have EC activities on your CV, potentially some part time work etc. If you're at a campus university, not commuting, and therefore can engage more with the opportunities a university offers you there is a good chance you may well be a better candidate on paper despite a less prestigious degree.
I go to York and study Law, and fully appreciate that it isn't the most prestigious of law schools. However, I love the university, love the campus nature of it and love the collegiate system. Due to this I'm extremely happy at university and have been able to get involved in so much more than I would be able to if I studied in London due to monetary reasons. This is even more true if my alternative to York was commuting into KCL.
My advice would be that life is too short to be unhappy, so make a change. Study somewhere you'll be happy, get involved in everything you can and really fulfil your potential.