Car was impounded

if the driver is picked up for a driving offence that warrants impounding then the car will get impounded for 28 days regardless of who owns it.

Just gotta love those 'admin' fees, as crooked as.

25 sounds a bit like normal nz business practice.
I imported some containers and had a quote and told em when to pick up as per quote. They then shipped it to the depot in auckland before they brought it up here. then they said it has spider webs so i paid another 600$ for cleaning no problem. Then i get a shipping bill for 3700$
when the original quote was 750$ .
So i went there and said its 50 meters from your depot to the cleaning the quote is from auckland to whangarei 180km costing 750$ and you want me to pay now about 3 grand for 50 meter?
UH oh you have a quote . uh sorry for the mistake i paid 1200 in the end.
You can be sure you get shafted how ever they can . just imagin i had no quote .

Correct as above.
#1 Car is impounded for Driver issues
#2 Finance issues belong to the car, not the driver.
#3 Police don't act on finance repo's unless they have been called to help pick it up because of known violence issues with the vehicles location/ person in possession, but vehicle would go to finance holders yard, not police impound yard.
#4 Driver fines from the police stay with the driver unless the courts order the vehicle surrendered to help pay the fines, but thats another story on surrender of vehicle to pay fines.
#5 (fairly sure) The impound yard can only charge whats in law & I would suspect that if you challenged the extra charges (in court) from the day you requested the vehicle released, that they would have to back down if they don't have a dang good reason for the delays.

Id be careful to pay the account, on the clear understanding the amount is in dispute, and legal action will be following.

So then you can get the vehicle, and raise the issue with the disputes tribunal, as I think MrFixit is correct. And I also think that any delays where they were mucking you around about releasing it, may be something a disputes tribunal would not let them charge for.

as above unless in #4 Judith Collins has the car crushed

That rule got changed a few years ago, I still have a car that has dual registered users but subsequent cars have had to be in one person's name

I spoke to NZTA and they are not aware of any admin fees. I also called other towing companies that impound cars for Police and they also said they don't charge admin fees, it's just the towing and storage fees as per legislation. I've spoken to Consumer Protection who have advised the same, dispute it now, if they don't budge, pay it in full (making them aware that there's a dispute and legal action will follow), then file with disputes tribunal over extra charges and lay a complaint with the commerce commission for breach of the fair tradings act. I have contacted them to reconsider the charge, as I have had advice from NZTA, Police and other impound lots that this is illegal so will wait and see what they say. It doesn't sound hopeful. I have to say, one company I spoke to Auckland guessed who the towing company is that is charging the extra admin fee, and she laughed and said "I'm not surprised", seems like they're pretty well know. Ironic that they're the contractors for Police impoundment but are breaking the law themselves :-/

Great follow up work.
Seems it's about time someone made that company fully aware of their legal obligations.