72 Hour visa free transit

Your segment:

UK - Shanghai - Macau

If you have mentioned your all stops within the itinerary you are definitely eligible for 144 hour visa free transit in Shanghai. 144 has replaced 72 hours in Shanghai years ago.

Also, if your return flight from Macau is:

Macau - Beijing - UK

And you do not have any additional landing, you will be eligible for 144 hour visa free transit in Beijing. There is no doubt about it. By the way, you are advised to print out your flight tickets as well as your hotel booking confirmation for at least for your first overnight in both Shanghai and Beijing on your return flight.