LON-SING-KUL-BEI-HK-LON

Hi. I think it's okay but would really appreciate someone double checking for me. Travelling London to Singapore, Singapore to Kuala Lumpur, Kuala Lumpur to Beijing, Beijing to Hong Kong. Then Hong Kong to London. We have 3 days in Beijing. All are direct flights without stops and I have a UK passport.
Could we use the 144 hr visa free transit instead of applying for a Chinese visa?
Thanks!