I went to an American School, and whenever I used Br English, it was wrong. But say I traveled to Britain with those as my schooling verification? Would I be wrong?
Many aspects of British and American English evolved differently, before the development of international media, because of the geographical separation between the two populations.
Today most British people are used to watching American films etc. If you come to the UK speaking American English, people will understand you perfectly well (apart from the occasional word which may cause puzzlement or amusement). However, if you were here for some time and needed to do any formal writing, it would be better to learn British spelling and vocabulary.