Kevin Rudd holds a strong lead as preferred Labor leader over Julia Gillard in today’s Essential Research poll, and Malcolm Turnbull has also overtaken Tony Abbott as preferred Liberal leader.

Thirty-two percent of voters think Rudd would make the best Labor leader, with Julia Gillard on 23% and “someone else” on 19% — none of Wayne Swan, Bill Shorten or Greg Combet get above low single figures. However, Gillard holds a commanding lead over Rudd among Labor voters, 51-31%.

And Malcolm Turnbull is now the preferred Liberal leader for 25% of voters, to Tony Abbott on 22%. The result was 23-22% in favour of Abbott in February. Abbott has gone backwards progressively since last September, when in the wake of his near-miss election result he held a strong lead over all comers. Joe Hockey has also edged up, and is now preferred by 17% of voters. But like the Prime Minister, Abbott remains the firm favourite of his own party, with 40% of Liberal voters preferring Abbott, to Hockey on 22% and Turnbull on 19%. However, interestingly Abbott’s support among Liberal voters has fallen from 45% in February, to the benefit of both Turnbull and Hockey.

Turnbull’s rise comes after renewed tensions within the Liberal Party following Turnbull’s comments on the Opposition’s climate change policy and a clumsy effort by Party Whip Warren Etnsch at disciplining Turnbull and other MPs for missing at vote. Turnbull took exception to Enstch’s email and the Liberals have been embroiled in a debate about the intent and timing of it ever since. However, the focus on the Liberals hasn’t dented their polling — the Coalition’s primary vote increased a point this week to 47%. With Labor (34%) and the Greens (12%) steady, the 2PP result returned to 54-46% in the Coalition’s favour, where it was three weeks ago.

Rudd’s strong polling — he held a similar lead in a differently-worded Essential leadership question in February — confirms that, in a manner similar to Turnbull, his ordeal of being deprived of the leadership appears to have erased much of the voter antipathy that built up during his leadership, which in Rudd’s case included the disastrous decision to abandon the CPRS. It comes at a time when Labor MPs are increasingly worried that Julia Gillard will not be able to turn around the party’s dismal primary vote level but MPs are concerned the leadership would be a poisoned chalice for whoever takes it.

Support for the Government’s carbon price scheme continues — in the absence of any details — to fluctuate, down again from last week’s high to 38% support, 48% opposition. Voters are also divided over whether there should be an election called on the issue, with 42% of voters supporting an election and 42% against — it was 40% support and 44% against in late March.

There was some better news for Labor on its brand, which polling has shown has been badly trashed on key issues in the last 12-18 months. Asked which party is best at representing the interests of different sections of the community, Labor led the Coalition strongly on people on low incomes, average incomes and welfare, and had small leads on families with children, students, indigenous people, ethnic communities and even pensioners. The Coalition only led on people with high incomes, big business (a massive 62-13%), small business, rural and regional Australians and “the next generation of Australians”.