Wow, I'd forgot I even made this thread. I'm in my final year now at King's, and I have to say I think I made the right decision. London is really not as expensive as everyone says, excepting the accomodation. You just have to budget a little more carefully. And there are massive advantages to being here. I did a work placement in my faculty this Summer, and met staff and students from UCL as well as King's, so it's so much more than just studying at KCL. You have access to the University of London, including the institute of Classical Studies library, and the University of London library (both in the same building), as well as KCL's own very impressive library. It's like going to two or even three universities at once.
Not to mention you have the British museum, and the Museum of London, and countless other things, on your doorstep. I swear that I would never have got a 1st Class mark in my 2nd year exams had I not been revising ancient Greek in front of the Parthenon friezes. I can just about read some of the temple inscriptions in there now.

You could probably say the same for Edinburgh as well, but I am currently studying Horace in Latin, and the textbook we are using was written by my tutor. And not just because he set it himself to make money: it's the
official Cambridge Classics commentary, the definitive book for the next 50 years on Horace. As in, there's nobody even at Oxford or Cambridge that knows as much about Horace as this guy.
Plus student life is pretty good. There's something for everyone, whatever you like: hard drinking, sports, quiet picnics, fierce political debates, ridiculously rich Arabs and Americans, local Londoners.... I don't actually know anyone at Edinburgh who studies Classics so I don't know how it compares, but I'll bet it's not as varied or exciting.
Criticisms:
It can be a little overwhelming at times, especially if you end up living in some ****hole of a neighbourhood because you can't afford to live in an area that doesn't have a crime rate equal to inner Sao Paulo's. I know a few people who have been mugged, and a lot of people who live very very far out and barely get to see their friends because they live at opposite ends of the city, or even go out in the centre.
Social life can be very expensive. Especially if you like clubbing. I once paid £9 for a pint of beer. In Scotland you would be within your rights to call the police if someone asked for more than £3.50.