I am a uk national. Is it possible to get my Chinese visa from the embassy in hanoi?

Imogen, you can possibly get the entry permit from this embassy. In addition to the ordinary documents required, you should also submit the original and photocopy of your entry permit or stay permit in Vietnam. I personally think it’s not very likely to get the 3-month type because you are applying in a third country. However, before making your decision, you can consult this issue with the officials on the spot.