I can't hep you regarding course structure etc. but I can talk about universities as best I can.
My reccomendation would be Birmingham. I know people who went there and said it was a great university. It is also Britains second biggest city by both population and size I beleive, while remaining cheaper in terms of living costs than London.
I don't know about fees for international students or what KCL's are but almost every cost of living (food, bills, transport, accomodation) in London is expensive, the average price of rent in London is currently £1,400 a month. Double the average in the rest of Britain. Brilliant, but expensive (I love London though). If money isn't really an issue then KCL could also be a very good choice.
I don't know anything really about Edinborough. I hear it's cheap but that was from someone who went there for 1 week so who knows.