How about this one?

Not BMC, it's a bigger truck.

Thornycroft

Not Thornycroft, BK.

Leyland

Leyland with a local (NZ) built cab ... Using what looks like Atkinson borderer/venturer/Defender windscreens

BK and werkhorse are right. it's a mouth organ grille 19.H/20.H Leyland Hippo. That's not a locally built cab though, it's an English fibreglass Homalloy cab made by Holmes (Preston) Ltd.
This is a 14.B Leyland Beaver with the same cab. Thanks for everybody for having a go.

You're probably right about the screens werkhorse. Holmes and Atkinson Lorries were both based in Preston, Lancashire. It would be late 1950s-early 1960s when these Leyland Beavers and Hippos with this cab were sold in N.Z. The Atkinsons with the Mk.1 fibreglass cab would have been introduced about the same time I would think.

The screens have a Foden look about them too.