I'm not that bothered about called a Brit. I think I must've used it about myself a good few times here. I say yanks quite a lot, but if anyone told me I'm being offensive by so doing I'd pack it in. At one time, on a long-defunct forum, I said merkins quite a lot, thinking that it was a Dubya Bushism. Then someone told me it meant a pubic wig. Tread carefully, eh!

Robin mentioned Paki. That has been used for decades as a directly offensive reference to "Pakistani" people (often ones who had never been to Pakistan). "Brit" carries weak or no really racist connotation, whereas "Paki" has done for a long time. They may both be similar shortenings but they carry very different sentiments.