Link to HSBC NZ
Income tax calculator
On arrival, apply for a NZ Inland Revenue Department Number (IRD).
Link to NZ banking and tax advice
If you will be paying tax abroad yet will be continuing to receive interest income from savings in the UK, you should fill out form R105 from HMRC and send it to the financial institutions where your savings are held. Normally tax is deducted from your interest income before you receive it.
This form requests that tax not be applied in future because your income will be taxed in your new country instead. If you don't do this, you may find that this part of your income is taxed twice.
[source - tax planning section]