New Zealanders have a reputation for being a bit cliquey and hard to break into as a social circle. However, I would argue, that this is very normal, and the same over there, as it is here. We've found that barring fellow expats and family, and work colleagues, then people are lovely and friendly, but not inclusive, if you know what I mean.
Try to be respectful of the differences. We are a bi-cultural nation, with a proud indigenous people, the Maori, who are enjoying something of a renaissance, in terms of arts, influence, their language - Te Reo, their place in history, and in particular political influence at both a regional and national level, particularly in matters of environment.
There's a lot of Brits, and some are wonderful, and some - not so much. A bit like Kiwis and Aussies in the UK! If you don't bang on about how superior the UK is (outside of the home - we've told our girls you can always come home and sound off inside these four walls, lol, because all ex-pats have times of frustration and homesickness, particularly in the face of indigenous smugness), and are appreciative of the positives of the country you've chosen to emigrate to, and that has been kind enough to receive you, it goes so much better.
My girls are thriving in this school system, and I hope your young one enjoys his time in NZ.
I remember a friend of mine from school, who joined our school at twelve. He was very much accepted, cool accent and a leather jacket. His singing was bloody appalling though. Wham, no less. (It was the eighties. . .) He was a lot more confident and outgoing than the more reserved Kiwi kids!