JEREMY Corbyn is on course to be Labour’s next leader after private polling showed he had a near 20-point lead over his rivals.

According to the survey, the leftwinger is poised to top the ballot with 42 per cent with Yvette Cooper, the Shadow Home Secretary, on 22.6 per cent, Andy Burnham, the Shadow Health Secretary, on 20 per cent and Liz Kendall, the Shadow Health Minister, lagging behind on just 14 per cent.

The one-person-one-vote system involves using second preferences should no one gain a simple majority of 50 per cent plus one vote.

Once second preferences were taken into account, the private polling gave Mr Corbyn that majority of 51 per cent; two points ahead of Ms Cooper.

In an attempt to stop the Corbyn bandwagon, some Labour MPs are now actively encouraging supporters of Mr Burnham and Ms Kendall to swing behind Ms Cooper, ensuring they either switch their first or second preference votes to her.

Earlier, Mr Corbyn described his embarrassment after women on an internet website branded him "very sexy" and "attractive in a world-weary old sea dog sort of way".

The bearded 66-year-old London MP's blushes came as he launched his policies on gender equality with a promise to have a 50 per cent female Shadow Cabinet and "work towards" ensuring half of Labour MPs were women.

Policies in Mr Corbyn's Working With Women document included forcing companies to publish equal pay audits and moving towards universal free childcare.

Speaking on Woman's Hour, the Islington MP criticised the media for focusing on personalities rather than policies in a race which has already seen Chuka Umunna, the Shadow Business Secretary, withdraw his candidacy because of the scrutiny directed at family members.

"It is very sad that some sections of the media are incapable of engaging in any of this at a political level and engage in it solely at a level of personal intrusion and personal abuse," said Mr Corbyn. "Does it hurt those around me? Yeah, it does," he added.

Ms Kendall told Mumsnet the contest sometimes “felt a bit 1970s or even 1950s” following controversies over whether the women candidates were strong enough to lead the party.

"I'm a feminist; women should be judged by their ideas, their values, and what they have to contribute, not by what they wear, what they look like, or their family situation or relationships," added the Leicester MP.

Elsewhere, Mr Burnham told an audience in Leeds how he proposed extra taxes to pay for a social care system that mirrored the National Health Service.

“I am determined to make Labour the party that helps everyone protect what they've worked for. The only way we can do that is to extend the NHS principle to social care, where everybody is asked to make a contribution according to their means and when everybody then has the peace of mind of knowing that all their care needs, and those of their family, are covered,” he added.

Ballot papers for the leadership contest go out on August 14; the result is due on September 12.