I've done London / New Zealand about 30 times and I've tried almost every carrier / routing.
By far the best in my view is LHR/ Hong Kong / Auckland on Air NZ. (I won't bother with anyone else henceforth!) It's about the shortest, premium economy is very nice and not expensive, the service is excellent and the brief stop in Hong Kong is easy, unlike LA which is dreadful if you go that way round. Departs LHR @ 21.30(ish) and arrives AKL 11.15) In my experience, going via Oz just takes longer, and for no benefit and one more stop.