Well, I haven't taken any upper division history in the US, yet, nor have I finished my applications and gone to the UK. I've done US general education, and yeah, its boring, but I mean, it really can relate to history, and offers ways of looking at history and understanding the major figures and ways of thinking. That said, I plan on finishing my degree in the UK as well.
I don't think curriculum wise it would be a very big difference, except for well, in the US you generally have to take a section or two of US history, and the in the UK you generally have to study some "British History" but the structure of the degrees really depends on which university you are talking about.
Obviously, Cambridge's tripos and the tutorial system is nothing like the huge lectures at Royce Hall in UCLA, so UK can be more personal, but in the US, the liberal arts colleges are designed for that purpose, and the large universities have seminars, which resemble the tutorials.
There's always study abroad, which would enable you to take a "general course," as LSE calls it, in the UK.
Ack, I'd write more, but I've got to head to class...General Education requirement to satisfy!! (first day of Second year English!)