Upvote:2
To re-enter Britain you need two things.
As I understand it your proof of residence is associated with your Italian passport which is expired.
The obvious and foolproof approach is to carry both your passports with you. Use the unexpired NZ one where it works. When you return to the UK present both. Based on your Italian passport Immigration can determine your residency from your Italian passport whether it is expired or not.
If the UK knows about your NZ passport it's likely they can check your residency status based on it. But for the tiny extra effort of carrying a second passport versus the possible complications if they can't, I would carry both.
It may be wise to renew your Italian passport.