I'm considering going to New Zealand for university, however I want to drive my car on its current UK plates while I'm there. Is it possible?
Yes, you can, for a while. (Not long enough to get a degree, though.) From Number Plates on the NZTA site:
Overseas visitor registration plates – on vehicles brought in by visitors. So long as the vehicle displays plates from its home country, visitors’ cars can drive on New Zealand roads without paying registration and licensing fees. The vehicle must remain licensed in its own country, but have a current New Zealand warrant of fitness (WoF) or certificate of fitness (CoF). The car owner must also pay the ACC levy. This exemption is allowed for 18 months or until the vehicle is sold or if the visitor becomes a permanent resident in New Zealand.
You will need to submit a Notice of temporary vehicle import by overseas visitor (MR2C) form.