Ok, so I managed to get this booked! Sounds like there was some married segment logic going on in their system which meant the flights weren't being shown online.
MEL-SIN - available online
SIN-LHR - available online
MEL-SIN-LHR - not available online (but available on the SQ website, so wasn't a married segment issue there)
Anyway, on the phone to the agent she got the same result. But said yep I can book it as one ticket for you. Then the problems came.
She said the points total would be 157,000 per person, 65,000+92,000. I.e. it would be priced per segment. It then got interesting in that I said "no, it should be 139,000 as per your points tables". She then proceeded to tell me that they are always priced per segment and wouldn't budge. I said, you calculate the individual segment miles and add them together and then price them as per the zone table. It is only priced separately if there is a stopover.
She was adamant that no, this was never the case and the points tables were only for direct flights and it wasn't possible for London. I tried to get her to search their own website which shows 139,000 on available bookings and she wouldn't do it. So I asked to be transferred to a supervisor.
Whilst on hold she spoke with a colleague who corrected her, so she came back on the phone, apologised and said she would have to manually override the systems points calculations.
Anyway, at the end of the day it was all booked! Happy days! But it shows that you have to be persistent with this stuff, I was a mouse click away from transferring the points to SQ and costing myself more points and $500 in infant fees! So a good saving.