Yes, you can add stopovers and split the legs, as long as there’s availability for each leg. Avios amount may change breaking the journey in SIN, but then you have the option to book different aircraft using the BA11/15 and BA12/16

I’d check manually for availability by searching

EDI-LHR on chosen date
SIN-SYD on chosen date

If this shows for you online call up and book as one booking. Example here:





Not sure how you’re confusing them, you should call and ask for the above or similar itinerary by flight numbers, dates and knowing before you call there’s availability