HK-Beijing-Singapore-Bali-hk

We are a family flying into HK for 5 days and then flying to Beijing for 3 days ( 68 hours) - flying to Singapore for 1 night - 5 nights in Bali and then back to HK FOR 1 night before flying back to Heathrow
Do we need a visa ?
Or If if we just fly HK- Beijing - HK - BALI - HK - LONDON - do we not need a visa
Have left it too late to apply for a visa and for a family of 5 it is nearly £1000 for the visa and am trying to find a cheaper option