CRUCIAL factors: A) What's your romantic status with this girl? B) What would you like it to be?
Can't believe nobody else had the good sense to ask.
If you're already with her, or you're not hoping to change your friendship, find her something SHE loves. First, figure out exactly what she loves about England and go from there.
Maybe she likes the fashions? Hard-to-get perfume from an English designer? If it's the art scene, she might like a book, poster or print from a small-gallery. Does she love the 'twee' factor? Something kitschy, like a bowler hat. Or maybe a map of London to hang on her wall (it would be strangely exotic over here). Whatever it is, figure out her connection to the place, then find something to embody that spirit in a playful way.
Get her something stylish she will find easy to put to use (even if that just means displaying it). There's nothing more embarassing than a present you don't know what to do with.
The girls in this city tend to be quite specific about what they eat, so I'd steer clear of 'treat foods'. Jaffa cakes don't exactly scream class, anyway. Fortnum's hamper might do it, at a push. Expensive, though.
If you're not involved with her, but are trying to seduce her, my advice is don't try too hard to figure out what she likes: be assertive, and get her something YOU like. Your gift will say "this is a piece of my world." You should be the most exciting thing coming from London, and the gift should just be a reminder of that.
Besides, if you get her something she really loves, she'll realise she can get great presents from you without having to sleep with you.
In all cases, don't get her anything she needs, obviously. It should be a treat. And stay the hell away from jewelry. Nothing says "I'm out of ideas" like something shiny and expensive.
If she doesn't have a teddy bear, she won't want a teddy bear.