It wasn't, however the association with Great Britain is undeniable, especially when Lesser Britain doesn't even refer to Ireland any more (in Roman times it did), but Brittany, however "British Isles" was in use by the Greeks (at least Prettanic Isles) before even that - well before the union of England and Scotland, never mind Ireland's conquest.

Personally I'm happy with Atlantic Isles/Islands/Archipelago as I agree the term isn't great due to the implicit association, but it's not like it was something just made up by colonists.