There is no such thing as a "British accent" - Britain is made up of England, Northern Ireland, Scotland and Wales. There are literally hundreds of different accents spoken across the whole of the British Isles. The accent that people are most commonly referring to when they say "British accent" is an accent spoken in some parts of south east England.
The south east accent is the one most frequently heard outside of Britain in the media and in films (curse you Hugh Grant!) so people don’t really hear many different accents from across the British isles which has led to the stereotyping of the "British accent".
Hugh Grant, Austin Powers, that guy in Oceans 11 (Worse "british accent" impression EVER).