Actually, the FCO office in Beijing has the same information on their website. It is now standard policy throughout China because of new passport issuing rules. The passport is sent from the UK, posted to HK, and then sent to your address on the mainland.

http://ukinchina.fco.gov.uk/en/help-for-british-nationals/passports

Taken from above site (pasted below):

We no longer issue standard (10 year) British passports at this Embassy. You now need to apply for your passport at our Regional Passport Processing Centre in Hong Kong.

Not doubting you have done it in the past, I also got a passport from Shanghai in the past, but whether it is cost cutting, less admin or for whatever other reason, you can no longer get a British passport from any consulate/embassy of the UK on the mainland anymore. Hong Kong is the processing centre for British people on mainland china.

Again, nothing personal, and nor I am in anyway involved with the FCO, just reporting my last experience and the current situation.

Respectfully,
SMGS