British citizenship of people born in Hong Kong

I need to know the citizenship at birth of someone with the following circumstances:

- Born in Hong Kong in the mid 1970s (ie before the 1997 handover and before the British Nationality Act, 1981 and after the Nationality Act, 1971)
- Lived in Hong Kong until migrating to the UK in the early 90s
- Currently holds a HK ID card with no expiry date
- Has a "Certificate of Registration as a British Citizen" dated 1996
- Holds no other citizenships and has never held any other citizenships

My understanding is that while there is a 1996 dated Certificate of Registration as a British Citizen, they are a British Citizen by birth.

Any ideas?

Edit: As they hold a permanent HK ID card, they are currently a citizen of the Hong Kong SAR of the People's Republic of China, even though they do not hold a HK SAR passport.

However there was no such thing as a HKSAR-PRC citizen at the time of birth or the time of Registration as a British Citizen.

So were they a British Citizen at birth?