I don't think so, Chris. My own tastes are fairly British - though I myself am not, I'm an economic migrant - and though most of my DVDs are American (reflecting the actual number of films that are made), I've got about 100 British ones, plus another 100 or so that are (non-British) European.
And although there is of course much American cultural influence on Britain - via TV and movies especially - there are more differences than many people suppose. Democrats and Republicans aren't Labour and Tories, for a start. Your views on, for example, employment protection would be much more at home in America, where sacked people are, as Tebbit suggested, expected to get on their bikes and look for another job (though they have Cadillacs instead of bikes). British sentiment on the subject, as I think you've agreed more than once, doesn't tally with your own.
It doesn't make you American, though, much less European; I think you're still basically British, and I'm partly so through long residence rather than nationality.