"British Isles sounds lovely"

And a very ancient term it is too but it is not describing the same thing. British Isles refers to the entire archipelago hence also includes the Republic of Ireland - and of course as another poster pointed out some Irish dislike the said term. Perhaps because they think of it in a political way whereas it is in fact a purely geographic term. The official term for the parts of the British Isles which constitute the UK or are linked to the UK politically is seemingly the "British Islands" though I've never actually heard anyone use it.