There are significant benefits that could be gained by transferring your UK pension fund to New Zealand:
You can receive all of the money from your pension as a tax-free lump sum benefit in New Zealand, instead of being compelled to purchase an annuity with the majority of the fund total, as would be the case if the pension remained in the UK.
You can access all of your funds but only if invested in a Kiwisaver from age 65 currently, although this may change with the official age of retirement. Should you wish to access funds at age 55, other New Zealand QROPS are available which would allow a 30% lump sum payment after 5 years of non UK residency with the remaining amount being used to provide your retirement income.
You would gain much greater control over how the funds are allocated where you will not necessarily have any input into how your UK Pension is invested or indeed whether the fund(s) into which your money is invested meets your personal investment profile.