https://www.immigration.govt.nz/opsmanual/#42601.htm
A2.10 Acceptable travel documents
A2.10.1 United Kingdom
Any valid British passport is acceptable if it contains the following:
the endorsement 'Holder is entitled to readmission to the United Kingdom', usually on page 5 (page 6 for British Subject or British Dependent/Overseas Territories Citizen); or
a visa to enter a third country after travelling to New Zealand; or
a separate certificate indicating right of abode in or re-entry to the home country; or
a residence class visa for New Zealand approved on the basis that the need to seek deportation would be unlikely to arise.
Note: If a passport does not show the right of abode in or re-entry to any country, the application must be referred to the National Office of INZ before a residence class visa may be issued.
A2.10.5 British passports in current use
(f) Passports issued after 1 July 1987 that describe the holder as a British National (Overseas)
Must have either: the endorsement 'the holder of this passport has Hong Kong permanent identity card number (xyz) which states the holder has the right of abode in Hong Kong' or
a Returning Resident entry certificate for the UK