leaving the country
Unless you have dual citizenship or end up applying for and receiving residency here in New Zealand, you are not eligible to join KiwiSaver.
See this link here for more on who can join KiwiSaver.
If you do end up becoming a resident and decide to join KiwiSaver but end up moving back to the U.K. at some stage, you would be eligible for early access to your KiwiSaver funds. This isn't the case if you're moving to Australia as under the TransTasman Portability agreement (set to go through before the end of the year) the money will be locked down until 65. It'll be up to you to decide which side of the Tasman you want your funds to be domiciled.
If you returned to the U.K., you would be permitted to withdraw all your savings, any returns, plus the kick-start of NZ$1,000 however the Government will retain the member tax credit portion, that is the NZ$521 max a year you receive from the Government.
Do be aware that it's not a simply a matter of rocking up to your provider and asking for a cheque. There is a mandatory stand-down period of 12 months during which you'll be required to present documentary proof of you having permanently moved. The details are explained further on the KiwiSaver website here under the early access provision.
I hope this answers your question.