If pressed, I would say I feel British. It's where I grew up and where I choose to live, the culture that I love, but I feel perfectly at home in America, I don't feel like a tourist or anything.
We used to get on planes, and they'd ask who we were, and we'd say, 'The Dave Brubeck Quartet', and they'd say, 'Who?' In later years they'd say, 'Oh', which amounts to the same thing.