If you go to the British Embassy website you can find a link to the Hong Kong consular office, with forms you can download and information about photo sizes and quality.
I couldn't be bothered to go to a photo shop to have the pics done, and as we had all the equipment here Mr.VS took some snaps of me (with a white background) and we made sure all the measurements were OK. Job done - photos printed and trimmed. Sent everything off to HK on Friday 3rd September, got my new passport today! Really good service from the consular in Hong Kong, EMS and DHL (from HK to here).
It was certainly less hassle than travelling to BKK and the total cost for the courier service was under 1,000 baht.
Now all I've got to do is transfer my visa from the old passport to the new one. Oh, no. A trip to the immigration office in Nakhon Pathom.

VS.