There was once a product which claimed to taste like butter called I Can't Believe It's not Butter.

In New Zealand, we now have a Government which looks like a Labour-led Government called the I Can't Believe It's Not a Labour-led Government.

NZ First leader Winston Peters has expended some energy trying to eradicate the pesky phrase "Labour-led Government," claiming it is not a true reflection of the coalition arrangement.

Instead, he has instructed media, MPs and anybody else in earshot to refer to "the Coalition Government" or the Labour-NZ First coalition government.

He will tolerate the addition of "with confidence and supply from the Greens" but only three times a year and only if uttered in a dark windowless room with no audience.

Even Ardern gets jittery when the three words are uttered in her presence.

Asked if she had asked ministers to stop using the term, she replied "ah, I've never used that phrase, I don't believe I've used that phrase.

"I tend not to and I'd expect [ministers] to refer to us as a coalition Government or a Government with a coalition partner and a confidence and supply partner."

The media merrily ignore Peters' edict and some may use the term in front of him just to annoy him.

National sometimes obeys him but only because they prefer "NZ First-led Government."

That was particularly the case over apparent differences of opinion on issues from refugee quotas, employment law reforms, the three-strikes law, and the Crown-Maori relations portfolio.

Peters has had some success with his eradication campaign.

The offending term has now been removed from the Beehive website and replaced with Coalition Government.

Ardern said that was not her doing.

"If you're questioning whether or not because there was a change whether or not because there was a change on the website that I'm ceding power, the answer is no."

Nor did the outlawing of the words "Labour-led Government" mean the Government was not led by Labour.

"I am a Labour Prime Minister, I am leader of the Labour Party and I am in a coalition Government. There is no doubt I don't think that I am the Prime Minister and leading this Government."

That at least is one thing the two agree on. Speaking on RNZ's Morning Report on Monday, Peters' advised listeners "of course she's driving the car."

Confusingly, he then added a further mode of transport into the mix: "There's only one captain on a boat."

As one minister summed up the situation "'Labour-led' goes without saying. That's why we don't say it."