> a very English idea
The UK didn't even have the worst public opinion of the EU in Europe on average.
Public polling has generally shown other countries - including Italy, Greece and France - have an approximately similar (or worse) opinion of the EU than we did. There's a significant chance that Sweden would have ended up having a referendum on membership if we hadn't, but how terribly it's gone for us has put off many of the eurosceptics elsewhere. During the worst of the Eurozone crisis, there were many who genuinely thought that the entire bloc would - or should - collapse.
I also think people here do understand it's a set of compromises. The question for many is whether the set of compromises has become too large and unwieldly. The common view of eurosceptics in the UK was that the scope had crept too far, and that we could gain most of the benefits through a normal trade agreement without having to compromise on aspects like agriculture, fisheries, immigration control and ceding control over national law and third party trade. I think so far this is not going well, but it's still an open question.
What you point out about Brits not understanding EU press is touching on an major issue a lot of people had with it: how can a supranational institution taking over national government function be truly democratic if you don't even have a standard language, and can't understand each other's press? A common aspect of countries with poorly functioning democracies is they don't have a common culture or language. Whenever I've needed information about the EU, it's always been difficult to find because the EU websites are poor and the source material is often in French or another language that I can't understand.
I absolutely agree that the compromises are necessary for the EU to function in its current state. However, perhaps the EU scope has become too large given how disparate the members are? If your partner desperately wants to live in Europe and you desperately want to live in the USA, does it really make sense to compromise by living on a boat in the Atlantic? Or is it better to just be friends instead...