Nope. We're called limeys for a reason
.
The new
Sims 3 expansion pack that I just got.
British is fine, but never English. Most will be fine with it, especially if an American does it. But if an Englishman called an Irishman 'English', there'd be trouble. Oh crikey yes.
'Britain' and 'British' are for the Home Countries: England, Scotland, Wales, and Northern Ireland. 'English' is passable for people from any of those places, but only just, and probably only by foreigners.
The British Isles is the general assortment of islands in that general area type place.
Great Britain refers to the biggest island. It's split into three countries: Scotland to the North, Wales to the West, and England.
Ireland is split into two countries: Northern Ireland to the North, and the rest is the Republic of Ireland.
Now, the UK incorporates Scotland, Wales, England, and Northern Ireland (and an assortment of other smaller places and islands), so it's full name is the
United Kingdom of Great Britain and Northern Ireland.
Phew.
Wikipedia has a sexy diagram that sums it up: