Personally, I think it's a mix between a lot of things:
1. We're a seperate island. I know Copenhagen is an island, but mainland Denmark is still on the mainland, and Copenhagen is closer to the mainland than much of Britain, and it's still a very "Eurocentric" city.
2. Much closer ties to America than other European nations.
3. Own currency, still use imperial measurements, driving on the left, etc.
4. Foreign policy differences.
5. There's the "British" ways of doing things. Judicial, Parliamentary systems, etc. are very unique and different whencompared to most places in the world - systems only really used in Commonwealth nations (for obvious reasons).
6. Still holding on to the good days when Britain could hold its own.
7. Linked in to #6, the UK still has much more influence over international affairs than most countries in Europe, and in most ways, the EU as a whole - and it is more likely to go against the EU grain than say France and Germany and do their own thing.
These all play a part. As well as general ignorance - most Brits probably couldn't even name most of the countries in Europe. When I went to Andorra, for example, most didn't have a clue where that was, sometimes it's just easier to say "Skiing in Europe", or "skiing in the European country Andorra".