multiple visa free options for UK citizen

Hi , I'm a UK citizen planning a trip and want to try to use the free option in several locations. Can I fly London to Hong Kong and stop in Shanghai for 4/5 days? Then can I take a trip return to Guilin from Hong using the 72 hour waiver option? Finally can I fly from Hong to London, stopping in Beijing and using the 72 waiver option for this journey?
Thanks you for your advice.