My secret: I don't even know what difference it will make if UK separates from EU.

Context: I visited the UK in summer 2014. At that time, I observed that a) I had to cross customs to get there from another EU country (but not from Ireland) because it's not part of Schengen. b) They don't use the Euro. c) They don't use the metric system. d) They don't speak multiple languages. e) They're not even physically attached to the European continent, map wise.

What exactly does EU membership even mean to the UK? They were obviously, at best, only half-hearted members anyway. Free trade? Whatever, you can have free trade agreements without being in the same federation. Military agreements? Different EU countries seem to have their own militaries anyhow, I think. Human rights? Lots of countries (see: Canada) do fine on human rights without having to federate first. The right to be forgotten? Okay, now I'm just being snarky.

But seriously, I really don't understand. This seems very minor. If, say, Germany left, that would be another story, since they seem to be all-in on the EU. I see no signs that the UK ever was. People seem pretty upset, so I'm obviously missing something. Can someone enlighten me?