I refuse to be called either English or British. I'm European and proud of it. (I never stand for the UK's National Anthem, which calls for a god I don't believe in to 'save' a monarch I refuse to acknowledge. I'll always stand for 'Ode to Joy').
However, irrespective of our differing opinions, all UK citizens are 'officially' called 'British'. (i.e. that's the convention used for census returns, etc). That applies even to those who live in Northern Ireland, which isn't part of 'Great Britain'.
Chris