72 hour visa advice

Hello,
I plan to visit Thailand, then Beijing, then Hong Kong and then back to the UK, are you able to tell me whether or not my stay in Beijing needs an entry permit please. I arrive in Beijing on the 2nd and leave for Hong Kong on the 5th. I am technically only in Beijing for 3 days as we just want to quickly do some sightseeing before heading to Hong Kong. My flights are both booked but with different airlines, can I still use the 72hour free transit this way?