I don't really understand why people feel the need to learn speaking English with a British accent, and from what I understand they usually mean English when they say British. What is wrong with speaking English with a Chinese, Spanish, Arabic, or, God forbid, a German accent? Language is about communicating with others, and as long as you have a good knowledge of vocabulary, have a good grasp of grammar rules to string a few comprehensible sentences together, know enough idioms and collocations to make what you are saying sound more natural, then that's really all what matters. After all, what are the poor devils supposed to do who speak English with an American accent? Or try to convince somebody from Scotland that they need to speak with an English accent. You will soon find out what they are wearing under their kilt when they turn their back on you.
I personally find it rather charming to hear somebody speak English with their native accent. It makes me want to know more about them, where they come from, their culture etc. Isn't that the beauty of the English language that you can make friends with people all over the world, even though you might not be able to understand each other's mother tongue? When a native English speaker gives you stick because of your foreign accent just ask them how many foreign languages they can speak.