Disruption is expected at Heathrow airport on Wednesday when public sector union members take industrial action over planned government reforms.
International flights to Britain could be halved in an effort to avoid queues and chaos.
The airport company said passengers are likely to be delayed so long at immigration that they might have to be held on board the aircraft.
BAA said this would quickly create gridlock at the airport, mass cancellations of departing aircraft and diversions of arriving aircraft.
Air New Zealand says it has only one flight from Auckland to London that day and it will fly as scheduled.
Even so, it is contacting passengers on that flight, offering them the opportunity to change to another flight if they wish.