If you were simply going to NZ and back I would second the suggestion of flying Air NZ. The "issue" is the addition of Melbourne.
Two possible solutions. Look at a round the world ticket. Talk to an expert agency like Trailfinders. Apart from the options offered by the "Alliances" (oneWorld and Star both work for your trip and Air NZ is part of Star) they can often put together a combination of other tickets at a competitive price.
Second, buy an Air NZ ticket London/Auckland/Hong Kong/London. Then buy a separate ticket from New Zealand to Melbourne and back. Now, note I said New Zealand/Melbourne. You should be able to buy (for example) Christchurch/Melbourne/Auckland. You can price this yourself using the Air NZ website for the UK/NZ piece and then (separately) Air NZ or Qantas or Jetstar(?) or Virgin Blue(?) or Freedom Air - you might have to price the trans Tazman as 2 one ways rather then a round trip. Alternatively ask an expert agency (another is Travelbag).
In either case use the phone (you can ask questions and dither about much more simply on the phone than the net) as well as your browser.