There is no such damn thing as a British accent. Only non-Brits would ever use the phrase, and then usually to mean an English accent. There are Scottish, English, Welsh and Northern Irish accents, which are each accents from Britain, but no British accent. Really. I promise you.

There are an astonishing number of regional dialects and accents currently in use in the British Isles, and even more that are extinct or near extinction. It's partly due to the flexibility of the English language, interaction with neighbours and immigrants, and the historical diversity of cultures within the country. I know of an anecdote that holds that a trained linguist can determine the birthplace of a Briton to an accuracy of 40 miles just by listening to the way they pronounce certain words.