Thank you for clarifying that. I was under the impression that the EU exerted some authority over England, but I guess that’s just not the case.
It is kind of confusing, so unless you live here and have the crazy visa rules, you wouldn't need to know or bother
But basically you have the European Union which consists of 28 states that basically tries to co-ordinate what they do and prevent wars between themselves (at least that was the original aim, right now it's a bureaucratic nightmare)
These consist of nearly all countries in the geographical construct called Europe with the exceptions of
The best diagram I found on wikipedia
The Eurozone is a sub-group of the EU which consists of states that share a common currency -- the Euro.
I see the trade benefits of the euro -- it means less currency conversions, but also the bad side without political union -- you can consider it to be analogous, but not similar, to the US with different states having one common currency (but the difference ends in the sense that the US federal government has more control over states than the EU council does)
Anyway, so the UK is part of the EU but not part of the eurozone, which makes sense to it. Cameron and most other British politicians "political expression" is to leave the EU but remain in something like the EFTA which is what Norway and Switzerland are in. But that is stupid -- because Norway still has to follow European Union rules and laws (to some extent) but has no vote at the EU meetings
Better to leave all relations with the EU and be like the USA dealing with the EU
But that is not good for the UK either due to multiple reasons:
Finally, to your point that the EU exerts some authority over the UK, it does -- but that's a very weak authority, so that the UK can reject paying fees asked by the central authority.
btw, also note that “England” isn’t the same as the UK — England is just one of the 4 nations in the UK, the others being the Scots, the Northern Irish and the Welsh