I went to summer school in London in 1964 and I stayed with a family. That was 50 years ago, but seeing how conservative the British are, I think it's a safe bet that families still take in students.
And as for what to see in London, don't worry. I'm sure her hosts will tell her all the places she should visit (and her classmates will take her to all the places she shouldn't).
Lol! Yep. Yeah it's normal for families here to take on foreign students. It's more common with European students (simply because they're closer I suppose) and usually it's an exchange. For instance my cousin recently had a German student stay with her and then she went back with her to stay with her family in Germany.
There's tons of sight-seeing in London. Museums, monuments, etc. Does Britt like musicals? The West End would be a good experience to catch a show. Something like Phantom of the Opera has been playing in the same theatre for years and you can virtually pop down anytime for an afternoon matinee rather than only a Saturday night or something.
Getting around London is an experience too. Manic, but strangely easy and logical with the subway trains. You can get all over the city in no time.
Gunnar has been far more than I have, but I suppose that's usual when it's on your doorstep!