Ms.Hammond, you can apply for a China visa in Chinese embassy in Hanoi. Please submit the below documents to the embassy during its office hours in person. You can also entrust a travel agency to do it on you behalf.
1. Your original passport;
2. One filled Visa Application Form of P.R.China.
3. One recent taken passport photo glued on the Application Form
4. You train ticket to China
The fee is 30 Pounds for China Single-Entry Visa for UK Citizens in U.K.. I don't know the fee for you in Vietnam. Maybe it is 30 dollars. The embassy usually need 4 working days to process visa application. You needn't a visa to Hong Kong and can stay HK for up to 180 days.