5 weeks off for NZ alone is definitely a good idea!
It's a big country with lots to see and do.
The thing I can help most with is the cheap bit of December. It's usually up to about the 9th. But availability is absolutely dire in the last few days before the cutoff point, as you can imagine, so get in early if you want to travel about then.
I think your options from MAN would be SQ and EK. Beware of EK's 777s, though - 10 abreast in economy although with a better-than-normal pitch make up for it.
All other reasonable choices (incl SQ and EK) go from LHR. Don't forget to compare going east with going west. If you go west, you can now connect onto a NZ at San Fran instead of necessarily having to go to the zoo at LAX.
Although it's too late for you for this trip, there is a way of getting 10% off the base fare of every BA flight. Buy 200 shares, and then wait till you're on the register on a record date (usually early Nov) to get the discount for the following year.