Firstly there is not one British and one American accent.People in London sound completely different from people in Yorkshire or in Scotland or Northern Ireland,which are all part of Great Britain.The same is true of the USA which is a vast country that has many different accents.You can look on youtube for many examples of this.Try this video where an actress does 21 different accents (not all of them are native speakers of English but most are)https://www.youtube.com/watch?v=3UgpfSp2t6k

Try listening to the British English and the American English audio recordings of the same transcript here: http://www.breakingnewsenglish.com/1505/150522-airbag-recall-l.html What differences can you hear?