English, Welsh, Scottish, I guess this sort of applies to some Irish?
They still don't. According to the 2011 Census:
a majority of people in England, Scotland and Wales pick English (60%), Scottish (62%) or Welsh (58%) as their sole identity
(Source)
I don't know about the stats for Northern Ireland, but I guess there's a large Protestant/Catholic divide; the former would identify as British or Ulster Scots and the latter as Irish.