There is no direct air route from Glasgow to New Zealand, but there are one and two-stop services you can catch to several Kiwi airports. You can fly to Auckland via Dubai with Qantas and Emirates in about 29 hours, or with two stops with KLM and Air France in about 30. Alternatively, Emirates also fly to Christchurch with a plane change in Dubai in about 30 hours.
If Wellington is your final destination, then you can catch a further connecting flight with Emirates from either Auckland or Christchurch, which should only add a maximum of three hours to the journey. To ensure that you find the best flights for you, consult ourflight search tool before booking.
There are similar services as mentioned above departing from nearby Edinburgh, but the fastest route to New Zealand is the Malaysia Airlines flight from Heathrow to Auckland via Kuala Lumpur, which should only take around 24 hours to reach its destination. There is also a similar service from Heathrow to Christchurch offered by Singapore Airlines.
The busiest time to holiday in New Zealand is the peak summer period of December to February. Because of this, the best time to visit if you want to save money but not compromise on enjoyment is around late-February and March, when the temperatures are still extremely pleasant, but the airfares are greatly reduced. Also, watch out for cheap fares in January and September, when many airlines have their biggest sales.
If the bigger New Zealand cities aren't your final destination, you may find it cheaper to look for cheap flights to Auckland say, and then either make use of long distance buses to complete your journey or book a cheap domestic flight yourself. While indirect flights may be available, they can be very costly.