Ack, of course you're right, and I knew this (United Kingdom of Great Britain and Northern Ireland, duh), and now it's driving me nuts because I can't remember if I got it right or wrong in that conversation with the student. Because we talked about the full title of the country, and I'm much more accustomed to saying "the UK" anyway. Not that students manage to grasp a lot of nuance anyway (so glad I'm not judged too much on what students think I said), but I, too, am pedantic enough that I want to make sure it was right--more so in class than in LJ comments, apparently! :)