We are british citizens and will be flying Manchester-Amsterdam connecting to Beijing

You need a visa or you need to change your flights. AMS-PEK-AMS isn’t a transit. Assuming you are flying with KLM, you could contact Air France/KLM to see if you can change your flights to MAN-AMS-PEK-CDG-MAN or MAN-CDG-PEK-AMS-MAN, neither of which would require a visa.

Your other option is to add in a side-trip out of China, for example PEK-HKG-PEK or PEK-SEL-PEK.