UK/Australia/New Zealand Reciprocal Health Care Agreement
If you are an Australian or UK resident, certain forms of medical treatment are covered under a Reciprocal Health Care Agreement. For more information, please see the following page; http://www.health.govt.nz/new-zealand-health-system/eligibility-publicly-funded-health-services/reciprocal-health-agreements
Note: As not all medical treatment is covered under this agreement, it is still essential that all foreign visitors to New Zealand have adequate travel insurance to cover the duration of their stay.
In New Zealand, Accidents are covered by ACC, this includes visitors. Information on such coverage is available here: http://www.acc.co.nz/making-a-claim/am-i-covered/ECI0002#P83_5873
NZs healthcare system is available for non residents, but you will probably have to pay. It is strongly advised that visitors obtain appropriate travel insurance, especially if you have ongoing medical issues.
In the event of a medical emergency, contact the ambulance service on 111.
Non emergency medical issues
For minor non emergency issues, the LCA staff may be able to help, or point you in the right direction.