another-view
Ah - but they are British.
Remember - British is a nationality. It's what it says on your passport. You don't have degrees of Britishness. It's a binary concept. Either you are or you aren't.
Perhaps what you're thinking of is the concept of 'Englishness', a subject explored by Kate Fox in her (excellent) book 'Watching The English'.
The book deals with what makes the English who they are (queueing, social embarrassment, hard work, non-earnestness etc). These are English traits, many of which apply to new Britons (and their children).
However, 'Britishness' is something completely different. The BNP will have a real problem separating those two concepts, because once they say they're fighting for the British, the next natural question would be 'What? All British subjects?"
Then they come unstuck.