Fully valid NZ PPL is usable in this country for day-vfr rentals, providing your renter wants it to be so! (you'll need a rental checkride like anyone else).
Conversion to JAA PPL - medical, skills test, ground exams (how many depends on whether you have 100 hours total time or not).
Both questions answered on
http://www.higherplane.flyer.co.uk/faq.htm (numbers 4 and 25 amongst others). If you need a NZ medical, I know Dr Perry in Hampshire is authorised. (See '1' in same site)