I feel like the idea of being British has been foisted on me. I'm black British, family from Jamaica.
My grandparents had a very weird relationship with Britain seeing it as some kind of pinnacle of culture, education and civilisation and being proud to be associated with it. My granddad was incredibly proud that he'd served the British empire/commonwealth in the second world war, for example. They treated Britain like some kind of maiden aunt - big, stoic, proper and someone to be on your best behaviour around to not let the side down.
I don't recognise this version of Britishness - sort of Britishness by association.
Similarly, I don't recognise the sort of Britishness I'm encouraged to have, black British, where I define myself as British but also keep hold of the culture of my Caribbean heritage. My Caribbean heritage is, to me, tied up with empire, slavery and my grandparents' weird pride in Britain. I don't want any part of that.
I don't really define myself as British, it just happens to be where I live because of all sorts of twists and turns of history and, therefore, I can't be proud of it. If history had played out a different way, my ancestors might have been stolen from their African homeland and taken to South America and I'd now be, say, Brazilian! Or, even more mind-bending, they might not have been taken from their homeland at all 
BTW, Britain isn't at all tolerant, multicultural or fair 