I think people are mis-reading the question here. Yes geographically yada yada the UK is part of Europe, but that's not really what's being asked.
As a Brit, I see no shame in being European. As far as continents go, it's pretty awesome. Alot of history and progress is made in Europe. Plus - it's nice to have somewhere warm to go if the weather gets a bit crap at home. But, like a few people here I believe there's a difference between being a continental European and...well British. I object to Brussel's increased influence in domestic politics and the bureaucracy that entails. I don't appreciate the ammount it costs us British tax payers. I don't want the Euro. I don't want the EU to continue expanding at the rate it is. Cutting ourselves off completly would be foolish, but nobody seems to be able to find a middle ground acceptable to the British voter.
I'd say we're European by definition, but not in spirit.