May be cheaper from DUB or AMS. UK taxes will be less

MM LHR-CMB,NRT-HAN,SIN-MEL,BNE-ZQN,AKL-GIG-EZE,LIM-UIO-GIG-LHR There are problems with your itinerary. Click ignore errors.
Great circle map

There must be flights between the airports. You have problems in South America : 4 flights maximum. Fixing and adding/deleting some airports gets MM LHR-CMB,NRT-HAN,SIN-MEL,BNE-ZQN,AKL-SCL-GIG-EZE,LIM-UIO,GIG-LHR

Note MileageMonkey is not up to date, so may be giving errors