Irenejg wrote: ↑Sat Dec 24, 2022 2:20 pm
it's probably fine for me to travel on my New Zealand passport
That should be fine as New Zealand passport holders are not visa nationals and so the airline will allow you to board a flight back to the UK even without a British passport or visa. Then, at the UK airport, you can speak to the Immigration Officers and explain your situation. There will be a delay, perhaps even of a few hours, on the return at the airport as the Border Force verify your details, but you will be allowed in.
The issue with the OP in the thread linked to in the opening post was that the recently naturalised citizen was a visa national and in a situation where the airline would not let him board without a British passport or a visa. And British citizens can't be issued visas. So he could not get to the Border Force at the UK airport to speak with them.
Irenejg wrote: ↑Sat Dec 24, 2022 2:20 pm
My plan was to apply for my British passport in New Zealand.
That bit is the bad idea. I would suggest staying in the UK in between your trips for a sufficient period of time until you get your first British passport. You can then take a longer sojourn abroad.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.