On the same £65,000 gross, a worker takes home roughly $2,179 more per year in New Zealand than in United Kingdom. That gap reflects the tax structure alone — before rent, healthcare, or savings behaviour come into play.
Housing is the first multiplier. New Zealand has very high rent pressure, while United Kingdom has high rent pressure. That means part of the higher take-home in New Zealand can be absorbed by rent if you land in a major city.
Healthcare and pensions go in the opposite direction. New Zealand runs a universal healthcare model — Universal public healthcare; supplementary cover is common. United Kingdom uses a universal model — NHS provides universal care funded from general taxation, with private top-ups. The country with lower take-home often shifts costs that the other country leaves to your private budget.
Net-of-everything, a relocation decision should weigh strong public welfare in New Zealand against strong public welfare in United Kingdom, plus differences in pension capture, social safety nets, and city-level cost of living.