144 hr visa free transit

Hi you website provides very useful informations. My planned trip will be
London - Beijing get 144 hr visa free then fly to Beijing- Hong Kong. From HK to London via 2 hr transit in Chengdu.
Will I eligible for 144 hr with British passport ? Bearing in mind my return trip will be HK -London with 2 hr transit in Chengdu.

Please advise. Thanks