At least, his wikipedia article says "Nationality: Irish". I certainly can't see him voluntarily taking British citizenship. To him we are the enemy. He doesn't take his seat in Parliament because he won't swear allegiance to the Queen.

Anyway, to understand the position you have to understand two things about the UK. The first is that we are not one of those nutty countries that gets all paranoid about people having more than one nationality. If you are British, we look after you, and we don't have a problem if another country also wants to look after you.

The second is that when it comes to Irish independence, we are like the pathetic ex-husband making doe eyes at his ex-wife hoping she'll come back to him. For this reason, we give Irish citizens all the same rights as British citizens. Even before we joined the EU, an Irishman could move to London any time he wanted without showing a passport, and immediately register to vote or even stand for Parliament. Not even when they left the Commonwealth and became a Republic did we turn against them.

(Incidentally, we also give the right to vote and stand for Parliament to Commonwealth citizens who live here legally, which is why Rebekah gets to vote. But Commonwealth citizens don't have a right of residence. So in theory we could have a Prime Minister who has to be deported because his visa expires . EU citizens, by contrast, get to live here but not to vote in Parliamentary elections, only local and EU ones. And to devolved Parliaments, if they live in a devolved country. So between her two passports Rebekah gets all the civil rights of a British citizen, even though she isn't one.)