Actually, not all British Passport were issued By the Immigration Department in HK. The older style Blue Cover British Citizenship Passport is not issued from HKID.
I still remember when i was a wee lad, my dad need to send the Passport Form to British Passport Office in UK to get his Passport Renewal. However, the british Passport Office will send your New Blue British passport to HKID for you to collect. Think the time was 198x, i don't really recall the time....
Anyway. MOST British Passport were issued and Renewed thru HK immigration Department. There are 5 type of british Passport you can apply for when you are a citizens in HK, depending on your Citizenship.
1.) BDTC (British Dependent Territories Citizenship) Passport. Issued to everyone born in HK before The July 1 1997 (but was not renewable from 1996 onward to HK Citizens. BDTC remain valid until 2002)
2.) BOC (British Oversea Citizens) Passport. Issued to person who are Not related to HK but acquired HK Citizenship before 1997. (Example, Commonwealth Indian living in HK)
3.) British Citizens (BC) Passport. Issued to Person who have British Citizenship either at birth, under war widow act, under Citizenships Act 1983 or Citizenship act 1996
4.) British National (Oversea) Passport. Issued to Person who have BDTC or BOC without the British Relations to replace respective passport.
5.) Certificate of Identity (CI) .Issue to person who cannot obtain any other British Passport.
Just want to point out one thing. Gary saying that BDTC were replaced by BOC It is incorrect.
ALL BDTC WAS REPLACED BY BOTC (British Oversea Territories Citizens) in 2002. Not with BOC
BDTC and BOC at any time have different Citizenship Definition.
參考: I was a BOC and registered to BC when i was really really young.