My family are flying from London HongKong Beijing then on to London

We have one week booked in Hong kong (BA) then fly Cathay to Beijing and have three nights in Beijing before home to London (with BA). I did this booking as was assured it was ok for 72 hour visa waiver with travel agent. Now booked and paid no one can say for definite that its OK! or tell me what to do other than get a visa! Concerned as never traveled to that part of the world and we have our daughters with us. Have contacted Cathy to advise - they never heard of 72 hour waiver. Having read your info I assume I should not worry......Check in with Cathy at HongKong airport and ask them for arrival departure card, then take special line when we arrive in Beijing - show return flight and hotel booking. Am I right - This has been the only website that has explained. Thank you