The prime minister has recovered slightly in the esteem of voters but still remains deeply unpopular, new polling from Essential Research finds. But she has pulled ahead of an increasingly unpopular Tony Abbott as preferred PM.

Gillard reached her nadir with voters in early September, when just 28% of voters approved of her performance and nearly two-thirds disapproved. Since then, she has clawed her way back to 37% approval and 55% disapproval — poor numbers but significantly better than mid-year.

Abbott, however, has gone further backwards with voters. Right through the year, Abbott’s approval rating has hovered in the high 30s — it was 40% in October. This week it is back to 36%, his lowest approval rating this year but not, in the scheme of things, significant. However, throughout the year his disapproval rating has been edging up, and has now reached 52%, his highest ever and not much shy of the prime minister’s level of unpopularity.

Worse, Gillard has overtaken Abbott again on preferred prime minister, for the first time since June, with a 41-36% lead.

Both leaders, it seems, are locked in a deathmatch of voter disenchantment, but Gillard has turned her momentum around, while Abbott is going the wrong way.

And for the first time this year, some evidence has emerged that Labor has stopped the rot on its branding and values, which has seen a systematic deterioration since the beginning of 2010. Essential re-asked a series of questions last asked in May about which party was better at representing various interests.

In May, little differentiated Labor from the Coalition for a range of interests, even those traditionally associated with Labor — families with young children, students, pensioners, indigenous people, ethnic communities. Now, however, Labor has kicked clear of the Coalition for all of those — 42-31% on families with young children; 39-27% on pensioners; 28-17% on indigenous people.

The Coalition only leads in representing the interests of “working people with high incomes”, “small business and the self-employed”, “big business”, “the next generation of Australians” and “rural and regional Australians”, although Labor has shrunk the gap on all of those except, interestingly, big business. Around 60% of voters identify the Coalition as the better representative of big business, compared to only 11% Labor.

If there’s any sort of Labor turnaround, it may have started in Labor’s base. Or, at least, the self-inflicted damage there has stopped.

Essential also asked about relationships with other countries. Voters seemed to have cool on foreign relations generally, with the level of importance attached to relationships down since March 2011 for every country except China. New Zealand, Britain and Japan were all downgraded by voters significantly — our relationship with New Zealand was rated as “very important” by 69% of voters in March, but only 61% now, for example.

But voter support for a closer relationship with China increased three points to 35%; similarly, support for a closer relationship with India increased by four points to 23%.

Support for a closer relationship with United States fell six points to 19%, but 63% say the relationship should “stay the same”, second only to Britain (67%). And 20 years after Paul Keating urged Australia to pursue its future in Asia, 74% of voters say out future is most closely tied to Asia, rather than North America (9%) or Europe (7%).

On voting intention, the slow Labor recovery of late has paused: the Coalition is up a point to 47%, Labor is steady on 35% and the Greens up one on 10%, for a two-party preferred that has levelled at 54-46%.