I really love Manchester, and it's only two hours or so away from London by high speed rail.

Everywhere is so close in Europe it's quite possible to hop a flight in the early morning, spend the day in a totally different language and culture, then take the evening flight back to London again.

I'd also add a vote for Germany, especially Berlin, though make it more than just a day trip if you're going to Berlin, it has truly amazing nightlife, even if you aren't into the pub/club scene.