Firstly I would say "no" but there is no such thing as "a British accent".There are many different variations. People in Scotland,Ireland,Wales and the North of England speak differently from those in the South and around London.Even within London there is a difference between different areas,and different backgrounds of people.If you watch the movie "Pygmalion" or "My Fair Lady" they explain the differences that existed between high and low class people,but even today that exists. So I would not pronounce them the same,but maybe someone else might find them similar.

Not really... the vowel in "won't" is the same as in phone, home and don't. The vowel in "weren't" is the same as word, third and burnt. They are clearly different to my ears. http://howjsay.com/index.php?word=won%27t http://howjsay.com/index.php?word=weren%27t