Since April 2015 KiwiSaver schemes have been unable to accept transfers from UK pension schemes, as they no longer have status as Qualifying Recognised Overseas Pension Schemes (QROPS).
However, Booster manages a superannuation scheme that does have QROPS status. This is the Booster SuperScheme which may be suitable for your needs.
From 1 April 2014, a change in tax rules means that if you transfer a lump sum from your UK pension scheme to a New Zealand QROPS, you will have to pay tax on the amount transferred. The amount of tax will generally depend on the length of time you have been resident in New Zealand.
We recommend that you get New Zealand and UK tax advice before making any transfer.