From Richard: 72 hr transit visa question for UK citizen

Hello, I am a UK citizen planning a trip all with the airline KLM as follows:

1. Birmingham (UK) >> Amsterdam (approx 3 hr transit) >> Beijing
2. Stay in Beijing less than 72 hours then
3. Beijing >> Amsterdam (approx 3 hr transit) >> Birmingham (UK)

Please will you advise if I can use the "72 hour free transit"?

Thank you.
Richard