Round trip but including HK on UK passport, can I still enjoy the 72-hour free transit?

Hi.

(UK Passport)

Thinking of travelling:
London -> Beijing (up to 72-hour stay)
Beijing -> Hong Kong (3 or 4 days)
Hong Kong -> Guangzhou (up to 72-hour)
Guangzhou -> London (direct flight).

Would that be OK taking advantage of the up-to 72-hour stay on each leg as I have flights out of mainland china both ways? (No vise for HK as UK passport).

Anything need to be done in advance? Do I need to register at a hotel in Beijing or stay with a friend who lives there OK? (Hotel for Guangzhou and HK fine).