Labour peer Harriet Harman has called for men not to stand in the next Labour leadership race, whenever that will be.

Talking to Sky News’s Electoral Dysfunction podcast, Baroness Harman said she would ‘encourage and support’ fresh male talent in the party, but would ask them: ‘Are you going to put yourself in front and put a woman behind you?’

Poor Andy Burnham. The new UK prime minister hasn’t even had a chance to warm up the seat of power and the Labour grand dames are already talking about replacing him.

Harman explained that she wants to ‘start the discussion about male ambition and male allyship’. She is hardly a lone voice in this regard. It seems there is a sisterhood within the Labour Party who are sick of men in leadership positions.

Most of these have complained about a ‘boys’ club’ at the top of the party, especially in the wake of the Peter Mandelson scandal. Indeed, Polly Billington, MP for East Thanet, has used the phrase ‘boys’ club’ so many times in interviews, even she must be bored of it. Earlier this year, it was culture secretary Lisa Nandy’s turn to moan that Labour had been operating as a ‘boys’ club’. She went on to complain that some of the No10 briefings against her female colleagues ‘have absolutely been dripping with misogyny’.

It’s all a bit rich. Many of the same women pointing fingers at Labour’s ‘boys’ club’ and calling for a woman-only shortlist for the next Labour leader, have often appeared not to know what a woman is. Remember when Harriet Harman said ‘women are women who are born women, but women are also women who are transwomen’? Which is as clear as mud. Or remember Billington, who took to social media to apologise for the Supreme Court ruling on the biological meaning of sex. She said it would cause ‘worry’ among ‘trans people’. It’s all very confusing. They insist that the next Labour leader must be a woman, while casting doubt on the meaning of womanhood itself.

Yet even if those Labourites demanding a woman leader did know what a woman is, a woman-only shortlist would still be a terrible idea. What matters most about a politician, leader or otherwise, is not her sex, but her own qualities and political views. Tory leader Kemi Badenoch has done well at the dispatch box recently, because she is confident and principled, not because she wears a dress. Margaret Thatcher may have been the first woman prime minister, but she is remembered for her achievements, not for being female – and she was certainly no feminist.

And who would be Harman’s pick for Labour’s first woman leader? Angela Rayner? Jess Phillips? Rachel Reeves? They’re hardly the most impressive of candidates. Rayner has only just returned to the cabinet after a scandal over under-paying stamp duty on a flat purchase; Phillips has made an almighty mess of the grooming-gangs inquiry; and we all saw what Reeves can do in power during her ill-fated stint as chancellor – that is, nothing positive.

Maybe this is all a ruse on Harman’s part. Perhaps the New Labour old-timer fancies another pop at the leadership, having twice performed the role in an ‘acting’ capacity – first after Gordon Brown stepped down in 2010, and then again after Ed Miliband walked away in 2015. For women’s own sake, let’s hope not. This is the same politician who thought riding a pink bus around the country was enough to woo female voters ahead of the 2015 election, and who praised Kim Kardashian for her ‘pioneering spirit’.

The likes of Harman can strike pseudo-feminist poses all they like. Labour has done very little to benefit women and a hell of a lot more to annoy us through its dogged denial of the reality of biological sex.

Right now, Labour might well be better off putting a red rosette on a donkey, male or female, and making it leader instead.

Ella Whelan is the author of The Case For Women’s Freedom, a part of the Academy of Ideas’ radical pamphleteering series, Letters on Liberty.