New Zealanders and the UK's health surcharge
New Zealand nationals are exempt from the health surcharge but will still need to complete a simple online process.

From 6 April 2015, people from outside the European Economic Area (EEA) visiting the UK for longer than six months will need to pay a health surcharge.
New Zealand nationals are exempt from this surcharge because of existing reciprocal health arrangements. However, you will still need to complete a simple online process to receive a unique surcharge reference number. Quoting this number on your immigration forms will help to avoid any unnecessary delay when processing your application.
Note: The exemption applies only to New Zealand and Australian nationals. It does not apply to people of other nationalities who may be applying for a visa from New Zealand.
To get a unique surcharge reference number, applicants should visit the Health Surcharge website and complete the online process.
For more details on the surcharge, what it costs (for those who are not exempted) and why it was introduced please see this document