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Ardern met the Queen in a sitting room at Buckingham Palace with her partner Clarke Gayford early today (NZ time).
She said rubbing shoulders with royalty had not changed her views on republicanism, but it was not something that she intended to pursue while she is Prime Minister.
Possibly the Queen had heard of those views - Ardern was presented with a gift of two framed photographs of the Queen and Prince Philip which she said she would take back to her office.
Ardern said being a member of the Commonwealth was not dependent on who the head of state was and she expected New Zealand would eventually become a republic but did not believe that would be any time soon.
Ardern said they had mostly discussed New Zealand, such as the recovery from the earthquakes.
She would not divulge further details - including whether they had discussed raising children in such positions - because it was against protocol.
"It's fair to say though that even before I went into that conversation that was something that was on my mind. Here was a remarkable leader who has conducted her life in the full view of the public and that has included her children. And there's something to be admired in that."
She gifted the Queen food items from New Zealand as well as a personal gift - a photo of the Queen on her tour of New Zealand in 1953 which was taken by a 14-year-old who was now in her 70s and had sent it into Ardern.
She had not raised the recent death of the Queen's corgi Willow because it had not felt right.
She is one of only four leaders to have a private audience with the Queen during the Commonwealth Heads of Government Meeting (CHOGM). The others are Canada's PM Justin Trudeau, South Africa President Cyril Ramaphosa and India's Prime Minister Narendra Modi who has avoided CHOGM for several years.
It is likely the Queen also raised her desire for her successor Prince Charles to take over as Head of Commonwealth after her own reign. The leaders are expected to decide on the future of that role at their Windsor Castle retreat tonight.
The Queen had raised it publicly for the first time in her address at the CHOGM opening although behind the scenes leaders have been quietly lobbied for years.
Ardern and the Queen had met more informally just before the meeting at a reception for the 19 new leaders among the Commonwealth countries - Ardern could be seen turning to the Queen, laughing and holding her hand up with her thumb and finger held slightly apart.
Asked about that afterward she could not recall the joke she had made: "I did make a joke about someone. It might have been Australia. Most of my jokes are at their expense."
Ardern will also make a toast to the Commonwealth at the state banquet.
It is a black tie event and Ardern is wearing a korowai and a Juliette Hogan dress. The korowai was provided by Ngati Renana (London-based Maori.)
"And I very thankfully have a friend in Juliette Hogan and she's made a dress that will accommodate my front pack."
That is what Ardern has started calling her pregnancy bump.