Can I use UK cash cards in New Zealand?

You will have no problem using your UK cash cards as long as they have a Maestro or Visa/Mastercard symbol, which pretty much every card has. Charges can be quite steep to take money out (around 1-2.50 pounds a time). If you are going with friends, it's a good idea to take turns taking large amounts of cash out then splitting it between you. This way the charges are spread out. You can also use your credit cards to buy items in shops easily.
It's worth knowing that Nationwide Building Society have no international charge on using their cards abroad, so might be worth opening an account before you leave.

Other Questions...

What's my luggage allowance?
What's the best transport option?
Is there wireless internet in New Zealand?
Can I use my mobile phone in NZ?
Should I take my laptop with me?