Last time someone tried to take a set of islands from the UK, they got beat pretty badly, and that was on the other side of the world. While its true in these past 30 years the British Military Power has shrunk, they are still sufficient to defend the UK and in the case of a build up to a world war you'd likely see an increase in the military

While I admit my countries armed forces is not the largest or best equipped, they are one of the best trained and have a lot of experience in the art of war.

If the islanders didn't want to to, the UK wouldn't let them be conquered. We are talking about invading the UK here, they wont be chuffed one bit and you'd likely see a full war over it as a result, and the UK is one of the most powerful countries in Europe and a major player in the world

And then, if the people don't want it, they are liable to resist. You would likely encounter non-compliance, 'mistakes' in tasks, possibly strikes, protests and maybe, more rarely of course, violent action (Or maybe that's just the Football yobs... Hard to tell...)