I'm no expert, but I presume it would depend on what degree you are transferring from and too. I'm pretty sure if they are similar degrees you would be able to cross-credit at least some of the papers. But the best idea would be to contact the university directly.
There's also the point that the time periods would be different. NZ uni goes from March to November, so there would be a gap between your UK end and NZ start.
All the best.
You can, but it will varying how many of your first year courses will transfer with you. You would also need to pay international tuition/fees. Best is to have the programme in NZ assess your transcript. Or proposed courses.