A slim majority of Australians say they would support an emissions trading scheme for the electricity sector, including 46% of Coalition voters, according to the latest Guardian Essential poll.

The new weekly survey of 1,797 voters says 51% are in favour of an ETS for electricity, and more people are undecided than opposed. Twenty per cent were opposed and 29% undecided.

The poll also indicates a legislative ban on political donations from foreign companies would be popular with the Australian community, with 74% of the sample in favour.

The latest Guardian Essential opinion survey has Labor comfortably ahead of the Coalition on the two-party-preferred measure, with Labor on 53% and the Coalition on 47%, which is the same result as this week’s Newspoll survey.

Last week’s Essential survey had Labor on 54% to the Coalition’s 46%.

While Labor is well in front in the national political contest, the trend for the Turnbull government in Essential has been more positive over the past couple of weeks. On 21 March Labor opened up a 10-point lead over the Coalition but the gap has narrowed over the past two surveys.

The slim majority support recorded for emissions trading in the new survey, released on Tuesday, follows months of aggressively partisan debate over climate and energy policy.

The Turnbull government countenanced an emissions intensity trading scheme for electricity last year, before ruling the option out after a brief internal Coalition revolt, where conservatives declared the government would not adopt any carbon pricing policy.

Since the government ruled out pursuing emissions trading last December, a significant consensus has begun to form in industry and among scientific experts that a market mechanism is the best option for creating investment certainty in the electricity sector, and driving emissions reduction, at least cost to energy users.

A string of peak bodies have already called for the adoption of a market mechanism, including the National Farmers’ Federation, the Investor Group on Climate Change and the Business Council of Australia, which explicitly called for an emissions intensity scheme.

These groups have been joined by the New South Wales Liberal government, major energy users, manufacturers and businesses including BHP Billiton, who have been supportive of a market mechanism to help drive the necessary transition in the sector to low emissions energy sources.

The current stakeholder consensus around carbon pricing is a major turnaround in a short period of time. Three years ago some of the same groups urged the parliament to get out of the way so that Tony Abbott could repeal the Gillard government’s “carbon tax”.

The latest Guardian Essential poll also indicates people are strongly opposed to all institutional and corporate donations to Australian political parties. The only form of donations supported by survey participants were donations from individual voters.

At least seven out of 10 respondents were opposed to political parties receiving donations from foreign companies (74%), casinos (73%) and property developers (70%). A majority of those surveyed were also opposed to trade unions making political donations (64%).

The survey also suggests Australians are dubious about third-party activist groups such as GetUp getting donations from foreign sources.

Thirty-one per cent of this week’s survey think that activist groups should be allowed to accept donations from foreign organisations or individuals and 41% think they should not be allowed, with 28% undecided.

The Turnbull government has flagged its intention to ban foreign donations to political parties and third-party activist groups.

The special minister of state, Scott Ryan, has said any overhaul of the rules regulating donations and disclosure for political parties must also consider the role of activist groups, such as GetUp, otherwise reforms would create an uneven playing field, and not serve the public interest.

A report from the joint standing committee on electoral matters recommended banning foreign donations to political parties and associated entities but the major parties split on the treatment of activist groups.

Labor says it cannot support the Coalition proposal to extend the fundraising and financial disclosure obligations imposed by the Electoral Act to capture all third parties that are in any way involved in public campaigning.

The Coalition members of the parliamentary committee were also critical of some activist groups campaigning while in receipt of tax-deductibility status – a position which reflects complaints from the mining industry about activism around the controversial Adani coalmine, and other projects.

The survey asked questions about whether donations to various groups should be tax deductible or not tax deductible.

A majority of the survey favoured tax deductibility of donations for a range of groups such as medical research organisations (76%), social welfare organisations (66%) and animal welfare organisations (66%).

But people were much cooler on churches and religious groups having that status (36%), and also groups that campaign on social issues (34%).

This week respondents were also asked whether they believed it was justifiable to break the law – a question which follows a declaration by the new national secretary of the ACTU, Sally McManus, that there is no problem breaking “unjust laws” such as rules restricting industrial action.

The response suggests Australians are law abiders by reflex, although the sample is divided. Thirty-seven per cent believe it is sometimes justified to break the law and 50% think it is never justified to break the law.

Those more likely to think it is sometimes justified to break the law were Greens voters (44%), other party voters (45%) and aged under 35 (42%),

Those more likely to think it is never justified to break the law were Liberal/National voters (56%) and those aged 55 and over (62%).