How do you talk in a British accent?

There is no "British accent"! I had an American friend once who concluded you're suppose to call it an 'English accent' because when you call it a British one "the brits get mad", well he was wrong to conclude that as well! Let me explain:
Britain is made up of England, Wales, Scotland and Northern Ireland; each of them have many many many different accents.

I think what you mean is "how do I sound like hugh grant/daniel radcliffe/ some posh english guy?"