Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
Can you tell me how long you have lived in the UK please. Is the pension you receive the NZ equivalent of the UK state pension?
Leave this with me while I draft my answer.
I just looked it up but thanks for the clarification.
You should refer to sections 5 and 9 of RDR1 here and the UK/New Zealand tax treaty here.
The NZ pension is taxable in the UK (see Article 19 in the tax treaty). State pensions tend to be taxable where the recipient lives as it would be impractical to tax or even trace most ex-patriot pensioners.
Your rental income will be taxed in NZ. If you choose to be taxed on your worldwide income as a UK national resident in the UK is or you bring the non-UK income into the UK, then you will pay tax on the rent in the UK but be given credit for tax paid on it in NZ. The same would apply to your small investment income. You could choose to be taxed in the UK only on that NZ rental and investment income you bring to the UK (excluding the pension) under the remittance basis of assessment (see section 9 of RDR1). You don't need to make a claim for the remittance basis to apply for any tax year where the un-remitted income for a tax year is under £2,000. If it is over £2,000, you need to complete a self-assessment tax return to claim the remittance basis of assessment. Credit will be given for NZ tax paid against a UK tax liability on the same income.
After you have been in the UK for seven of the previous nine tax years, you will have to pay the remittance basis charge of £30,000 for any tax year that you wish to be assessed on the remittance basis. Clearly, that will only suit the seriously wealthy with high non-UK incomes. If you choose to be taxed on the remittance basis, you may lose your right to the UK personal allowance of £11,000 which you can offset against your income reducing the tax charge.
I hope this helps but let me know if you have any further questions.
You can register using the form SA1 here.