I honestly don't know.
To be honest, it's not really a big part of my identity. The things I feel proud of by and large aren't particularly unique to Britain - I am awed by science, believe that technological and moral progress are both very real and attainable, and generally think that the human race shows a lot of promise.
I'm also very proud to come from a part of the world that champions freedom and democracy, which I think are both forces for good in the world. But that's not specific to Britain- that's generally a feature of Western culture as a whole.
The only uniquely British thing I can think of that I feel genuinely proud of is the English language. Having gone abroad to teach it, and studied a couple of other languages, I think English is a genuinely elegant and beautiful language, and in a way I'm proud of the opportunity that its extremely widespread nature offers - in a way, it's made a far greater degree of diplomacy and dialogue possible in the world just by being such a successful lingua franca.
I do also feel some pride in British cultural achievements - the incredible success of our academic institutions, and also our remarkable contribution to the performing arts.