I think everyone in this thread has brought up some really valid points...I'd listen to what they're saying.
In my opinion, I'd say go for an American college, exploit the heck out of their study abroad program, and go from there.
I was born in a small Georgia town, and moved to Brussels, Belgium when I was seven and we lived there for five years. My brother attended and graduated from high school in Belgium, and attended a US college. I moved back with my parents to a suburb in Georgia, I go to college in New York City, and I came back in May from a semester in London (which was great...partly due to the awesomely warm reception from MR members!).
I'm not saying it makes me an expert, but I've lived in a foreign country, been all over the US, and really considered going to college in the UK as well. From what I learned, it's going to be pretty difficult, especially since they have very specific entrance exams (from what I see... been a few years since I looked at this stuff).
Some things to think about:
1. Study abroad programs are amazing. Seriously, how often can you just decide to go live in another country for 4-5 months, and just go, and come back when you want? Without all the extra hassles? You can experience London, or any other place. Go live in London for 1, 2, 19 semesters...and I'm not just recommending it because I did it

I was able to intern while I was in London, which I loved, and I'm still working for the London company now that I'm back home...so you can always make helpful contacts while you're attending a US school.
2. Visiting isn't the same as living. Not saying you didn't get a good idea for London -- it's a great place -- but I'd say you haven't "lived" there until you hit the 6 month mark (I only was in London for 4 months myself). That's when it stops feeling like a vacation and you start noticing all the other stuff, too.
3. College is a big enough transition without adding culture shock to it. Not saying you can't do it, plenty of people do, just keep that in mind. My brother had a hard time (as an American) going to an American school coming straight from Belgium...again, he's not everyone, but something to think about.
4. Agree with everyone saying that the US is diverse, so make sure to check out everything it has to offer.
5. And, just to be a complete devil's advocate, if you really, truly, and passionately want to go to school in London...make it happen, cause this is the time in your life to do that
Good luck!