I’m perhaps a bit biased because for me a country boils down to a government, and I’m from the new world (we tend to see immigrants differently - more like “newcomers” and less like “outsiders”), but I’d consider you British.
That doesn’t say much though. At the end of the day, “you’re British” or “you’re Polish” seem fairly minor to me, compared with “you’re human” and “you’re you”.