You can actually ticket fully on OW airlines & partners with only one stop in SIN but you won't earn any TP's nor Avios on the SIN-AKL leg by doing LHR-SIN with BA/QF and then SIN-AKL with J* on a QF codeshare. I've done this earlier this year and won't recommend it because of the "easyjet" mode of transport that J* represent, and the lack of a VOD system on a 10 hour flight. Other than that it is a very FAST and smooth way to get across in a straight line.

Recently I've seen an offer on MH, LHR-KUL-AKL for only £830 in economy which is pretty good value