london - shanghai - hong kong - beijing - london ( with connection in shanghai ) 144 visa waiver

Hi - i want to stay in Shanghai for 4 days , then head to Hong Kong for 3 days, then head to Beijing for 4 days and then return to London ( flight goes to Shanghai first then onto London ) could I apply for a 144 visa waiver for both trips into China as on the UK government site it says going in and out of China Mainland via hong kong requires a visa