Thank you for all the suggestions! Unfortunately going to TPE won't work as transit to KHH is not straightforward and will add to the cost.

Oddly, it seems like if I do BCN-LHR-HKG-KHH and back, the price comes is at around 1000 EUR, as opposed to £1300 for LHR-HKG-KHH. That's almost £1000 saving for 3 people! So we figured we'll get RFS to BCN and spend a night or two for an extra break and still save money.

I've managed to get the itinerary below. I tried calling BA but the person wasn't very helpful, saying that there's no price, probably because of the CX long haul leg. Does anyone have any ideas on how to book this or what I can say to get the agent to book?

Thanks!