100% English, but that's only as far as I'm aware, and only as far as that means anything. Neither of which is a particularly long distance.
While England (and Britain, and the UK) isn't perhaps a melting pot in the same way the USA is, and it's never been the site of a mass pilgramage or anything, it's all just the product of what came before. I'm a little bit Celtic, a little bit Norman, a little bit Anglo-Saxon, and almost certainly a little bit Roman to boot. It's not really a measure of anything except how many generations I can count.
I feel more kinship with the Anglo-Saxons than the Normans seeing as I think of Great Britain as my home that they invaded, but once you count back so many generations, you'll have more ancestors than people have ever existed, so I owe as much to Harold's enemies as to his people. Not that it makes it any less interesting - I'd love to hear about my x*(great)-granddad the Roman general - but he'd almost certainly be ariich's and alirocker's and XJDenton's granddad too.
I'm only English, then, for as far as it's sensible to be precious about it. So that's barely at all, but also... completely!