A UMR poll the week after Todd Muller took over as National Party leader has shown no immediate change to the National Party's fortunes, although Muller has debuted at 13 per cent as preferred Prime Minister.

The poll results had National on 30 per cent – just 1 per cent higher than the 29 per cent it scored on the last such UMR poll under Simon Bridges' leadership at the end of April.

The poll has Labour still well ahead of National on 54 per cent, NZ First was on 5 per cent and the Green Party on 4 per cent.

UMR is the polling company used by the Labour Party, but this was one of a regular series taken for its corporate clients rather than Labour.

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Muller's 13 per cent support as preferred Prime Minister was higher than Bridges was on when he was rolled.

That was the same as Bridges' highest score in the UMR poll last November - but Bridges had dropped to 7 per cent by April as voters reacted to his response to the Covid-19 crisis.

Ardern was miles ahead on 65 per cent support as Prime Minister.

Muller's entry was not quite the "Jacindamania" when Ardern took over from Andrew Little as Labour leader on August 1, 2017.

In the first polls after that, Ardern leaped from 8.7 per cent to 26.3 per cent as preferred PM in a Newshub Reid Research poll done the week she took over.

A 1 News-Colmar Brunton poll two weeks later showed a larger spike for Ardern from 6 per cent to 30 per cent.

However, Muller is still relatively unknown and many voters are likely still making up their minds about him.

The poll of 1211 voters was taken from May 26 to June 1 and has a margin of error of plus or minus 3 per cent.

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It started on Muller's Tuesday of Troubles: the day on which Muller and deputy Nikki Kaye ran into trouble over the dearth of Māori in high-ranked positions in the reshuffle, and confusion over whether MP Paul Goldsmith was Māori.

The National Party leadership will have been hoping for a quick bounce in the polls for Muller, although his initial good start was derailed by those blunders in his first week.

They will be disappointed at the result and hoping that it simply reflected the instability that surrounded the fractious leadership change.

Muller has spent the past week pushing for the Government to move to level 1 more quickly, and pointing to the differences of opinion on Covid-19 issues between the PM and NZ First leader Winston Peters. He has claimed it is a sign of a "dysfunctional government".

The poll results are similar to other polls taken before the leadership change: the Newshub Reid Research poll had National on 30.6 per cent and the 1 News Colmar Brunton poll a week later put National at 29 per cent.

The Colmar Brunton poll was done while the leadership contest was rolling out – which will have affected the result.

It is understood National's caucus is yet to be shown any of the National Party's internal polling by Curia since the leadership change. Two sets of polling will have been delivered since Muller took over on May 22.

National was polling in the mid 40s in February, before Covid-19 hit the country.

Former leader Simon Bridges had previously dismissed the UMR polls because of the link with the Labour Party.