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But my I797 says my h1b nationality is Chinese, so i don't think i can use my British Passport to get the H1 visa right? because it doesn' match?

-It is fine for you to get the H-1 visa using the old H-1 approval notice (if not expire yet) and your British passport. Just explain to the IO about your nationality change if asked. Nationality change does not affect the H-1 approval and H-1 status validity (irrelevant).

So basically if I go to the UK with an expired visa on my Chinese passport I could be stuck there?

-You need to get  a new H-1 visa to come back using the British passport.