In May 2015, Kerry Abel wrote to all the Labour leadership candidates on behalf of the campaign group she chairs, Abortion Rights. She asked them to sign a petition protesting the harassment of women entering clinics. She hoped Yvette Cooper, known for her pro-rights stance, would sign. When she didn’t hear back, she emailed again, and again. In the end, only one candidate signed: Jeremy Corbyn.

Abel was among the women who gathered in the airy London headquarters of Unison on Wednesday evening for one of Jeremy Corbyn’s policy launches. Five months after Corbyn signed her petition, Abel reciprocated by joining Labour. She said: “He understands which campaigners are doing the work and will take the line from them.”

The room was full of campaigners like Abel – trade union activists, different generations of feminists, students. They were concerned about the future of services supporting women (86 per cent of cuts since 2010 affect women, according to the House of Commons). Again and again, they praised Corbyn’s anti-austerity policies. His condemnation of welfare cuts received booming applause.

According to YouGov, 67 per cent of Labour women back Corbyn, compared to 57 per cent of men. With his white beard and retro air, Corbyn is not an obvious feminist icon. But since winning the Labour leadership in 2015, he has embarked on an ambitious listening project. He has heard female grassroots campaigners more acutely than any other would-be leader. By contrast, his rival Owen Smith’s stated desire to “smash” Theresa May “back on her heels” went down about as well as Labour’s Pink Bus.

The most famous part of Corbyn’s listening project has been crowd sourcing questions for PMQs (he received 40,000 before his first session), but he is also setting up a Labour party Women’s Advisory Board. At the policy launch, he recalled what Tony Benn had told him – that it was almost impossible to get advice outside “the magic circle” of civil servants.

“There is a well of experience out there,” he told his willing listeners. “This is how you develop the policies to do things differently.”

Angela Rayner, a Corbyn protégé who is now holding both the shadow briefs for Education and Women and Equalities, embodies that voice. As Rayner told the audience, she grew up on an estate, raised by a mother who could not read or write. By 16, she herself was pregnant. Her journey to parliament included going back into education, working as a care worker on zero-hours contracts and entering the trade union movement.

“I was a NEET”, she said, before describing how she felt during a Westminster debate on deprivation: “I am sitting there listening to MPs talking about my life, in arbitrary terms and figures.

“What makes me upset is the Government is pulling up that ladder that helped me.”

Another view: If rallies are a barometer of popular support, why do the Tories win?

Corbyn is promising more funding to support domestic violence victims, protections at work and moving towards universal childcare. Many women I met at the event praised his policies. Liz Warren-Corney, a Londoner who now works in Glasgow, reflected on an earlier idea, from August 2015: “I know it was really controversial, but when he talked about women-only carriages, I thought actually it reflects an understanding of how dangerous it can be. When I used to get the tube to go to school, I travelled in the guard’s carriage.”

But despite his warm reception among women on the public service front line, Corbyn’s listening project can seem tone deaf at times. He has pledged to continue having a majority women cabinet, both in opposition, and in government. But female MPs such as Thangam Debonnaire and Lilian Greenwood have complained about his management style. Half of Labour’s female MPs signed a letter asking him to do more about social media abuse targeted at women.

When I asked Corbyn what he would do if, as expected, he wins the Labour leadership contest again, he struck a conciliatory note. “I obviously hope we do have a successful outcome in this election, but I recognise this is just the beginning of the process,” he said. “I want to reach out to all members of the Labour party and the parliamentary Labour party. I want to show them we are serious about the inclusion of everyone in the Labour project. That is the only way we can take on the Tories in the general election.”

Corbyn was speaking alongside one of his most high-profile allies, Diane Abbott. In time, more female MPs will no doubt respond to calls for unity, or at least the prospect of continuing work they are passionate about. Sarah Champion has already resumed her role as shadow minister for preventing abuse.

But others still appear deeply alienated. Chi Onwurah, a black, northern engineer, is a pin up for diversity and female ambition. She remains a shadow cabinet minister, but nevertheless backed Smith and, in a recent Staggers article, laid into Corbyn’s management style: “In any other job I would have called on my union for support in confronting an all-white management which prevented two of its few black employees from doing their jobs.”

To change the management culture, she argued, would take more than words. If a victorious Corbyn truly wants to work with the women of the PLP, he’ll have to listen harder than he’s ever done before.