I don't mean to question or worry you but, according to the JY website, the Heathrow departure on 18th October is via Singapore airport (on Singapore Airlines) to Auckland. The Gatwick departure on the same day is via Dubai (on Emirates). 

I'm sure you will get your final travel documents soon confirming the arrangements but both of the JY NZ tours that I have done were from Heathrow via Singapore with some of our group in February this year joining us in Auckland from Gatwick via Dubai.

Fingers crossed it all falls into place and you have an amazing time.

Happy Travels

MLB