We do not learn other countries' cultures in school, but in real life.... (Knowing the English call fries chips is taught in English class, but it's only vocabulary.)
If that's your question, American culture is far more widespread than British culture.
The Europeans don't learn English because of the culture, but because of the usefulness of the language. And it would be more accurate to say the Europeans learn American than English...
European countries have their own cultures and, sorry to say that, the UK is not known as having the "best" culture in Europe, compared to France and Italy for example.
Except the TV serie "Skins", James Bond, British rock/pop music and maybe Monty Python and Benny Hill, I don't known many British things particulary popular in Europe...
Remember, Europe is not part of the anglosphere, the only anglophone culture really influent on Europe and the rest of non-English-speaking world is the American one.