It wouldn't be a question of saying "are these people British" -it would be saying "do you want this piece of territory to be part of Britain" - or rather, part of the United Kingdom (obviously no part of Ireland has ever been part of Great Britain, which isn't a country anyway, it's an island.) There's no reason the inhabitants shouldn't continue to have full British nationality. And of course, no matter what, everybody in the European Union has a right to live and to vote in any part of the Union, regardless of which country's nationality they happen to have.