Hi,
As you have rental income from a UK property, you are taxable on this income in the UK in the first instance, under article 7 of the UK / New Zealand tax treaty.
UK/NEW ZEALAND DOUBLE TAXATION CONVENTION AS AMENDED BY THE PROTOCOLS SIGNED ON 4 NOVEMBER 2003
This income must be declared in a self assessment tax return (SA100) every year and on supplementary pages SA106 (property) to declare the rental income and expenes and SA109 (residence) to claim that you are not UK resident and entitled to claim personal allowances.
Any UK tax payable, should then be claimed as a tax credit in New Zealand. If your tax free personal allowance is more than the net property income, then there is no tax to pay, but a tax return is still required.You should consider contacting HMRC's 'Let Property Campaign' regarding the taxable rental income of the last 5 years.
Let Property Campaign
Thank you.