I think that to claim back the VAT you would need a VAT no, although I have no experience in that field, would think that what you claim as new at the UK end has to be claimed as new at the NZ end and the duty on different catorgory of goods varies.
They do check on things though so do take care, we know of one guy who had been collecting old Meccano for himself and brought the entire collection (about 40 to 50 boxed sets) over without declaring it.
Customs seized it and it was sold at auction here in Chch. the poor guy had to outbid others for it and ended up having to pay well over $2000 to get it back.