I don't think that being part of Europe, either in the present EU or in any future, equivalent body, necessarily means abandoning any of those things -- certainly not pride and self-respect, which all other EU nations have in spades even whilst being comfortable in the Union.
Churchill's opinion, meanwhile, of Britain's role in Europe was shaped rather heavily by his obvious fondness for our Imperial past. This isn't a criticism, but it's also difficult to see how exactly one can claim to be forward-looking whilst hearkening back to the "glory days" of Empire, which are now long behind us.
But anyway. I admire Churchill a lot, and despite all the undoubted faults in his character and views he remains one of my favourite politicians.