... I’m British and was born and brought up in the UK! :D
I assume what people mean by a British accent is ‘Queen’s English’ or ‘BBC English’ or ‘Standard English’, or whatever you may call it.
I think it’s certainly worth learning to speak English without a strong accent or colloquial sayings, as it will make you more understandable to more people, especially those speaking English as a second language.
No book can be a substitute for listening and repeating good role models. As well as films and TV, you could try listening to BBC radio on the internet – most of their output is available on demand for 7 days after transmission, and there are podcasts of some shows. Radio 4 probably has the best examples of proper spoken English.
And if all else fails, you could befriend a British person: we don’t bite… or at least not all of us :)
