I often get asked something like this, 'How can I learn British English?'.
And I usually have to reply that there is no 'British English' exactly. But instead there are many 'British Englishes'.
Each town and city have slightly different accents and colloquialisms. And sometimes even different dialects, my grandad used to talk to his friends with some kind of magic language that only they understood, full of slang and strange pronunciations. And in parts of England, Wales, Scotland and Ireland, there are even totally different languages.
For students I guess the question really means, 'How can I understand people when I go to the UK or watch British TV?'.
Becoming familiar with a variety of accents will help, but what I think might be more useful is learning some of the British phrases and idioms that people commonly use. My mum seems to talk mostly in idioms and colloquialisms, and I often think that non-native speakers would have a hard time to understand what she's going on about.
This recent article on The Independent (a British newspaper) website has some good ones:
One of the fun things for me in learning other languages is the unique phrases that you don't find in textbooks, this link has a lot of good ones.