Gardyloo, yes you are absolutely right. When it didn't show up for a particular day I didn't try days either side. Doh! So it looks like I can book this online after all.

FWIW Our itinerary is LHR-HEL-KIX-HKG-BNE-CNS-ASP-BNE-ZQN--AKL-SCL-GIG--GRU-LHR departing around 12 Jun and back around 31 Aug (for the kids to go back to school!). We will probably have to buy a couple of additional flights as we'd like to go to Salvador in Brazil too. When I first looked at this it seemed like an internal flight within Brazil would be a possibility on this ticket but they seem to have been dropped over the last few months.

Thanks for the help!