I get enough inquiries from people who ask about learning a British accent, that it seems to be important to clarify that this is too broad of a statement. Usually this inquiry comes from Americans who mean that they need to learn RP (Received Pronunciation), also known as Standard British. Here's a little more insight for you:
You can check out our current offering of accents from the British Isles to see what other related accents you might dig into as well.