Hopefully we withdraw fully from the EU, and the Euro collapses.
Just watch the Eurovision song contest for an idea of how ridiculously different Europe is from the UK, and how widespread the whole "we like them but not them" thing is.
I don't want to pull the wrong rope but how can you group cultures like Slovakia, Spain, Greece... and saying "we" are different.
Europe as a whole is a bunch of countries with different cultures that team up together to be stronger. The only common treat is the continent.
You can be happy that you aren't involved in the "saving the euro" mess and you should be. But believing that you are somewhat distanced from the EU or that it would be possible to believe is totally delusional - the european integration is extremely deep even if the euro fails and in my opinion cannot be stopped or reversed.
In addition, the cultural differences are not really that large. Europe has a common fascination with arguments and alcohol, especially the Northern parts (which include Uk, Ireland, Scandanavia, Netherlands and Germany). Historically, there have been huge links between the UK (and ireland) and these countries. To claim that there are these huge differences based on the Eurovision is a little absurd.
That being said, while watching the Eurovision i often find myself regarding them with a mix or horror and bemusement, but thats mostly because they're the kind of people who go on the Eurovision, not because they are of different nationalities.
The UK does have a problem though, in many ways we are much more like america economically than the rest of europe, but european is trade is big part of our economy.
It's fairly obvious that our countries usual musical output is pretty decent, and if we entered any of that into the contest, we'd win (If it was actually anything to do with the song).
I love the Eurovision song contest though, because it highlights how ridiculous the idea of integrating Europe is. You get countries who always vote for each other even when the song is rubbish, and you get no one voting for us, even when we have a half decent song. The Eurovision song contest is the best advert for a 'euro-skeptic'.