Most of the internship positions are in Washington, of course, but they do post some people overseas, in the more user friendly posts, however you're not likely to be the only person who thinks London sounds good. Part of the difficulty in getting substantive internships is the necessity for security clearances. Plus, the bulk of the internships are unpaid, and DC isn't exactly cheap. Housing overseas would depend on availability, but usually, they'll put you in something that's open until the next officer shows up. Check out Answer 2
you'd probably start by doing a search on a job search page....like i did when i came across the notice of brazil hiring a couple of workers, ,maybe one, in their DC embassy.
lot of cool jobs being offered on the net...