This paragraph from an article in the the BBC News Magazine summarizes the complexity of the British national identity:
The English are British and lots of people think the British are English but that annoys the Scottish andWelsh because although some think they're British and some think they aren't and some think they are but don't want to be, they all agree that they definitely are not English. The Irish mostly think they are Irish, apart from the ones who are Northern Irish. Some say that makes them British and Irish. But others disagree and say they should just be Irish and then some say they aren't British either but part of the United Kingdom. People from England, Scotland, Wales or Northern Ireland can all play cricket for England because they're British as can those from Ireland even though they aren't British. So can South Africans. The English play football for England unless they aren't that good when they might try to play for Ireland. Those from the Isle of Wight are English, from Anglesey are Welsh and the Orkneys are Scottish, but although that means they aren't from the island of Great Britain they're still British. The Channel Islanders depend on the crown which is what the Queen wears but they aren't in the UK and those from the Isle of Man are the same, apart from their cats.Actually, the entire article shines on various aspects of Britishness: accents, class, pubs, newspapers (and their puns), queuing, and self-deprecation - "an inescapable part of British discourse."
'Tis quite brilliant, actually.