Fifty-one per cent of voters believe the prime minister, Scott Morrison, should have sacked the Nationals minister Bridget McKenzie over her handling of the $100m sports rorts affair, according to the latest Guardian Essential poll.

The latest survey of 1,080 respondents, taken in the wake of revelations that McKenzie used a sports grants program to favour groups in Coalition-held or targeted seats, also shows voter support galvanising for an independent federal anti-corruption body, with 80% backing the proposal.

When asked about the conduct of McKenzie in allocating grant funding to marginal seats to favour the Coalition in the election, 51% said they believed the prime minister should have stood McKenzie down from cabinet over the issue, while just 15% endorsed Morrison’s decision to support his colleague.

About a third (34%) of participants said they had not been following the issue.

Coalition voters were the least likely to say that Morrison should have stood the minister down, with 41% of voters saying she should go, 27% supporting the prime minister and the remainder unsure.

The result comes after an explosive ABC report on Tuesday revealed that Sport Australia raised concerns that the Morrison government’s administration was compromising its independence in the weeks leading up to the election, and as the merit assessment scores of more than 2,000 projects were made public.

The fresh revelations will heap further pressure on Morrison to move against the agriculture minister, whose conduct is being examined by the head of the prime minister’s department, Phil Gaetjens.

The Essential survey, taken from 20 to 27 January, shows that support for McKenzie’s removal is higher than voter support in December last year for the removal of Angus Taylor from cabinet. At that time 35% of voters supported Taylor’s removal after police initiated an investigation into the doctored documents scandal.

Voters were also asked in the same poll if they supported the establishment of an independent federal corruption body to monitor the behaviour of our politicians and public servants, with 75% supporting the idea. This has since grown to 80%.

The number of respondents “strongly supporting” a new federal anti-corruption body has also risen, going from 42% in December to 49%, with support highest among Labor voters at 86%. Across all voting groups, only 7% opposed the idea, while 13% reported they were unsure.

The survey also tested voter sentiment about the government’s climate change policies, asking about a range of hypothetical policy responses that could underpin the government’s pledge to “evolve” its response to the climate crisis.

The most popular response was for the accelerated development of new industries and jobs powered by renewable energy, with 81% of respondents supporting the measure, including 75% of Liberal and National voters.

Almost three-quarters (71%) of those surveyed supported a zero-carbon pollution target to be set for 2050, but support was high among Labor and Green voters (81% and 89% respectively) and low among Coalition voters at just 56%.

When asked if they supported the prevention of new coalmines opening in Australia, the view of respondents split dramatically, with 48% of Coalition voters opposed to the idea, and 84% of Greens voters and 70% of Labor voters supportive.

Across all potential policies, support was higher among Labor and Greens voters, and lower among Coalition supporters.

The survey on climate policies comes as Morrison faces mounting pressure to explain how he intends to “evolve” the government’s climate change policies after he indicated the government would do more in the wake of the bushfire crisis.

The prime minister has conceded the severity of the fire season is partly caused by climate change, but has sought to shift the focus to “adaptation and resilience” and a “practical” response, rather than on emissions reduction measures.

In a speech at the National Press Club on Wednesday, Morrison will focus on the government’s “practical” response to the bushfire crisis, flagging a change to how the federal government can respond in times of national emergency.

Morrison will say that while it is appropriate for states to take a leading role, “where, when and how the resources and capabilities of the federal government should be engaged is less clear”.

“To date, the role of the commonwealth in responding to natural disasters has been limited to responding to requests for assistance from state governments. They judge the time and form of support needed,” draft excerpts of Morrison’s speech say.

“The scale of the bushfires this season – not least their simultaneous reach across state borders – has unequivocally demonstrated the limits of those arrangements.”

He will flag a review of the constitutional and legal framework to allow the commonwealth to declare a national state of emergency, the legal interface with the states and territories on responding to national emergencies, and an enhanced national accountability regime for natural disaster risk management, resilience and preparedness.

The Essential poll, released on Wednesday, also canvassed support for a new national day to recognise Indigenous Australians either to replace or to sit alongside Australia Day.

The survey found that compared to last year, support has decreased 2 percentage points with an overall 50% of respondents supporting the concept.

Of those surveyed, 32% supported including a separate national day with a further 18% supporting a replacement of Australia Day.

Support for a separate day was highest among Greens (73%) and Labor (58%) voters, and among those aged 18-34 (65%).

Young people in this cohort were also far less likely to celebrate Australia Day compared to last year, down from 45% in 2019 to 32%.

The poll’s margin of error is plus or minus 3%.