Labor has crept further ahead of the Turnbull government, and Bill Shorten’s approval ratings have improved in the wake of the super Saturday byelection results, according to the latest Guardian Essential poll.

The latest survey of 1,032 voters has Labor ahead of the Coalition on the two-party preferred measure, 52% to 48%, an improvement within the poll’s margin of error since the result last fortnight, which was 51% to 49%.

There has also been a three-point improvement in the Labor leader’s approval ratings. 34% approved of the job Shorten is doing as opposition leader (up 3% from last month), and 44% disapproved (down 3%) – a change in his net approval rating from -16 to -10.

Malcolm Turnbull remains comfortably ahead of Shorten as better prime minister, with 41% backing the Liberal leader and 27% backing the Labor leader. Turnbull is down a point and Shorten up two.

But the prime minister’s personal approval, which has been on an improving trajectory in the first half of 2018, slipped backwards, with small movements inside the poll’s margin of error. 42% approved of Turnbull’s performance as prime minister, down 1% since last month, and 42% disapproved, up two points – a change in his net approval rating from +3 to 0.

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The latest poll results come as MPs have returned to federal parliament after the winter recess, with many government MPs nervous about the recent rout for the LNP in the Longman byelection, with Queensland a key state in determining the outcome of the next federal election.

The new session has opened with the government in open disagreement. The government faces a noisy internal debate on Tuesday morning over the national energy guarantee, as well as continuing pressure from Labor in the parliament about a controversial grant to a private foundation for work on the Great Barrier Reef.

Ahead of Tuesday’s party room debate on energy, Turnbull and the man he replaced as prime minister, Tony Abbott, clashed publicly about the national energy guarantee, and Abbott used a television interview on Monday night to deny that he’d engaged in sniping or wrecking against the prime minister.

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Abbott told the ABC he had talked in this term about policy because he wanted the government “to be the best it can possibly be”.

As well as the energy stoush, a Senate debate over the rights of the territories to pass laws legalising euthanasia is also due to get under way on Tuesday. That debate is also causing ructions amongst government conservatives.

Respondents to the Guardian Essential poll were asked questions this fortnight about the drought, with drought assistance in the headlines in recent weeks.

Just over half the sample, 54%, believed the current drought is likely to be linked to climate change, while 25% think it is unlikely to be linked to climate change.

Voters most to think the drought is linked to climate change are Greens voters (80%), Labor voters (64%), voters aged under 35 (62%) and people with university education (62%). People not accepting the link were more likely to be voting for people other than the major parties, and older.

Voters were also asked questions about whether they approved or disapproved of governments giving financial help to industries. There was strong majority support for assistance for agriculture, renewables, health and tourism.

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Voters are more supportive of governments funding drought assistance than they were when the question was last asked in 2014.

There was also a question about media diversity and about free speech, given recent controversies about whether hard-right commentators should be banned from social media platforms.

Views on freedom of speech were mixed. 32% agreed with the statement: “Social media platforms should have to allow such people even if they don’t like what those people are saying, because those people have a right to free speech”, and 48% agreed with the statement: “An individual’s right to free speech doesn’t mean that social media sites must provide those individuals a platform to speak from”.

Voters were also sanguine about the recent takeover of Fairfax Media by Nine. Respondents were more likely to think the tie-up positive for the quality of news coverage and diversity of news media. The sample was split about whether the takeover was good or bad for jobs in the Australian media and news coverage in regional areas.