That would probably knacker you for NZ and quite probably Oz as well. Check out British Expatriate Community : British Expat Community for general advice or enz.org for NZ advice.
Get a permit to work in NZ, then after 5 years you can walk into Oz. Not my plan as I feel at home in NZ, but one that many people take.
Yet again, getting into NZ is easier with sponsorship.