Julia Gillard has pushed further ahead of Tony Abbott as preferred prime minister and the Opposition Leader has plumbed new depths of disapproval with voters, new polling from Essential Research shows.

In Essential’s monthly leadership approval questions, the Prime Minister has further narrowed her net disapproval gap, with her approval rating remaining at 41% and her disapproval rating falling two points to 49%. That Gillard is now into a single-figure net disapproval rating is a remarkable turnaround even from September, when it was nearly 20 points, let alone March, when it was nearly 30 points.

Abbott, however, has gone further backwards. His approval rating is down four points to 33% and his disapproval rating is up four points to 58%, giving him his worst ever net disapproval rating of 25 points. That’s still well shy of Gillard’s worst performance, however — at one stage she reached -36 points — which suggests he can still retrieve the situation with voters.

The Prime Minister’s lead over Abbott as preferred PM has also increased to 13 points, 45-32%, indicating she has decisively broken the long deadlock between the two leaders that saw them swapping small leads on that question for most of the last 18 months. Her lead is the biggest since February 2011, before the government’s carbon price commitment sent them plunging in the polls.

What appears to have happened is that much of the visceral dislike of Ms Gillard has vanished. At times the Prime Minister had well over 30% of all voters saying they “strongly disapproved” of her. That figure is now down to 24%, while simple “disapproval” hasn’t shifted anywhere near as much, and “approval” has steadily crept up.

And while Gillard continues to perform better with women — who are evenly split on her performance — than with men (net disapproval of -16), Tony Abbott has a huge problem with female voters. Both men and women don’t like Abbott’s performance, but this month his net disapproval among women blew out from -19 to -30. Gillard also now leads as preferred PM among both men and women, although among women she leads by a huge 21 points.

Gillard’s improved performance seems to be narrowing the gap between the parties, but only slowly. Labor’s primary vote remained at 37%, but the Coalition’s vote fell a point to 45%, on top of last week’s 2 point fall. With the Greens remaining steady on 9%, the 2PP outcome is now 52-48%.

Voters also indicated they saw the Gonski recommendations about increased schools funding as the most important reform currently before the government, with 31% nominating it as the most important, ahead of aged care resourcing (29%). The NDIS was nominated as most important only by 16%, with the Murray-Darling on 12%.

Asked to nominate preferred spending cuts to pay for reforms, slashing the Baby Bonus was by far the most popular option, with 53% of voters saying they favoured reducing the Baby Bonus to $2000 or eliminate it for people earning over $75,000. I

nterestingly, for all the claims of “class war” from the Opposition and the media, the support was almost exactly the same across Labor, Liberal and Greens voters. There was similar strong support for higher taxes on high income earners as the best method of increasing government revenue, with 46% nominating lifting taxes on high incomes, although Liberal voters (40%) were somewhat less likely to back that than Labor or Greens voters; 27% preferred no additional revenue measures at all.