The real problem is not the compatibility of gas bottle connectors, but of the incompatibility of gas.
A UK barbie will operate on one of either propane (red cylinder) or butane (blue cylinder), but you cant buy either of those gases here in NZ. Well, you can, but I was quoted over 400 bucks for a fill for a 9KG bottle of propane!!!!!
What you can get readily (just about every garage forecourt) is LPG, which is a mixture of butane and propane. So the official answer is that you cant operate a UK BBQ off readily available gas in NZ.
I brought a UK patio heater to NZ, and have sucessfully connected it to LPG, and although it sounds a little odd (different gas pressures) it operates reasonable well, though not as well as it could on the right gas of the right pressure.
If you are competent to make gas connections you can get what you need from several chains, but if you need to ask, then you dont know enough to do the job with a sufficient degree of safety.