Hi,
are you HCPC registered as a physio in the UK?

Although I cannot determine this with 100% certainty, I am pretty confident in saying that in order to register as a physiotherapist in NZ, you need to have a Bachelor in Physiotherapy. Your overseas education needs to qualify you as a physiotherapist in your 'own' country.
Registration in NZ is under a 'general scope', which requires you to demonstrate competencies in MSK, cardio-resp and neuro in theory and practice.
Check the Physioboard's website. There's heaps of information for baseline requirements, competencies/ threshol desriptions, etc.

You can work as a massage therapist, because in NZ, this is a non-regualted profession. I.e., no qualification required at all to hold that 'title'.

Good luck,
Fyzzio