Well, a lot of "British" names are used around the world, because of colonization, but the names that I associate as British are:
GemmaTamsinFelicityJaneGeorgiana ElizaIsobel
RupertAlbertArthurFrederickOliver
Jack,
Harry and
Sophie are all great names, but extremely popular in the
UK right now. I'd rather see a little
John,
Henry, or
Sophia that is nicknamed
Jack,
Harry, or
Sophie.