Taken from the Direct Line site.
If my No Claims Discount (NCD) has been earned in another country, is it still acceptable?
Only if it is issued by an insurer from an EU/EAA country (proof must be written in English). NCD earned in Australia, Barbados, British Virgin Islands, Canada, Faroe Islands, Gibraltar, Isle Of Man, Japan, Jersey, Monaco, New Zealand, Republic of Korea, Singapore, South Africa, Switzerland, USA or Zimbabwe is also acceptable provided it is written in English and the NCD level is shown in years and not as a percentage.
Many other companies should accept NZ/Australian no claims discount proof, but it will need to be from your last Insurers and will need to meet the same conditions as Direct Line.