Re: UK [...] does not have a proper written constitution.
"I'm not sure NZ can claim a "proper written constitution" either,"
The NZ constitution act(1986 one, not the 1852 one) was debated, modified, voted and passed, but not put into law before the parliamentary session ended for the year. It was supposed to be one of the first items on the agenda at the next parliamentary session.
Guess which bill mysteriously disappeared from the "put into law" TODO pile during that hiatus when it was realised that many things the NZ government and police do routinely would no longer be legal.