Glademaster said:Ireland is not part of Britain not even Northern Ireland.
Northern Ireland is part of the British Islands, quite a few N. Irish consider themselves British, even though the UK is a different thing, my mother being one of these people.
http://en.wikipedia.org/wiki/British_Islands
Northern and the Republic are part of the British Isles.
http://en.wikipedia.org/wiki/British_Isles
EDIT: Although I agree that people from the Republic should have and I encourage the non-British mentality.
People from Northern Ireland however are just as British as the Scots, English and Welsh, in my humble opinion.
DOUBLE EDIT: Saying 'British' is a lot easier than saying 'Person from the United Kingdom', even if all else fails.