The sneers show Harman has a mighty task

Her big idea - on which she expects to be judged - is to get half- a-million single mothers out to work

Paradox: we will only be able to dispense with a Minister for Women on the day the appointment is not greeted by sour whingeing articles proclaiming that we don't need one.

On Harriet Harman's appointment as Britain's first cabinet Minister for Women, The Daily Telegraph said she represented "an outdated ideology and the fruits will be injustice, social tension and further family break- up". They made rude remarks about her legs, plus this resoundingly idiotic maxim: "If women can get to the North Pole without any help from the government, they surely don't need any help from Miss Harman to survive in Britain." So that's why we still need a Minister for Women. And the first women's minister not afraid to use the f-word: she calls herself a feminist.

How will she fight her corner? Naturally, she says she won't have to, all being sweetness and light, for now. But she will "look over the shoulder" of all her cabinet colleagues, monitoring policies for their impact on women - and that will not make her popular. Every policy paper is already crossing her desk. Take last week: someone in the Treasury flew a kite that the Government might re-integrate couples' incomes for tax purposes, as a fall-out from merging the tax and benefit system. Imagine the headlines: Labour abolishes women's right to independent taxation! "It's just not on the agenda," Harriet Harman says crisply. "And it is not a necessary part of tax-benefit integration."

Indeed she is marching her department in the opposite direction. She has called for research on the distribution of income within families to show why women in couples drawing Income Support or the Job Seeker's Allowance should draw their own and their children's share independently. At present fathers or stepfathers draw the money and may not hand over enough. That would be a radical shift of most benefits, from wallet to handbag.

The poorest families are often not single mothers, but couples where the father keeps too much of the benefit for himself. Now that is the sort of change no male Secretary of State for Social Security was ever willing to contemplate.

Her big idea, on which she expects to be judged, is getting half a million single mothers with school-age children out to work. The plight of single mothers is an emblem for feminists, as their poverty reveals how powerless most women still are when not supported by a man. Most women if deserted by their children's father cannot support their families alone, because women's wages are too low for them to earn enough to be breadwinners.

But all will depend on the Treasury, for single mothers on benefit are not registered unemployed and are not in the pounds 3bn welfare-to-work initiative. The manifesto promises after-school child-care "in every area", which is what will make her initiative work. Does that mean a guarantee for all children? "No," she says cautiously. "It means in every area." How many, how soon and at what cost will be down to her bargaining power with the Treasury.

Opening another front, she is about to enter a scorching fire-fight with separated fathers. She is determined to force fathers to pay up for their children via the Child Support Agency. The fathers' Network Against the CSA, the most effective civil disobedience campaign for years, will be girding its loins again when it hears this: if she can't make the present system work she will change the law to make the formula for squeezing money from fathers more stringent. The Tories softened the formula in the face of father-fury but she is resolute: "It needs a cultural shift."

Her strength comes from knowing the way women live in her poverty-stricken constituency, Peckham in south London. Eyebrows will be raised when she says she will stop the hounding of co-habiting single mothers. "I want to say it doesn't matter what your relationship is with your boyfriend, what matters is what you can do. I want to take away the incentive to lie." That would be a revolution for many single mothers who live by subterfuge in fear of being shopped by neighbours.

What will she do with the Equal Opportunities Commission? It does not, alas, belong to her but to the Department for Education and Employment, though she says she will be involved. The clamping tight of lips suggests reform is likely, as the Labour Party has promised in the past. The EOC costs nearly pounds 6m, has been exiled to Manchester and, under the Tories, has been plagued with a deliberately weak leadership to keep it quiet. It beavers away producing reports of minimal public impact. Expect change here.

In elbowing her way to get women's issues on the agenda, she has a secret weapon. Anna Coote, the feminist thinker and her new adviser, will be the one to deliver it: her expertise is in citizens' juries and new ways to give democratic legitimacy to decision-making. Harman and Coote plan to enlist a huge bank of women of all kinds right across the country - ordinary women, not just the usual semi-moribund women's organisations. "It will be a genuine dialogue with large numbers of women. More women voted Labour than ever before at the election, but women distrust government and feel disconnected from it," Harman says. Establishing that contact - a kind of giant interactive focus group - will give her a huge advantage in bargaining for what women want, helping to keep the party in tune with its new female voters.

It is just as well that Harriet Harman was hard-baked in the political furnace when the row over her son's grammar school place very nearly sank her career. For she can expect considerable blow-torching from all sides - as can her advisers.

Take last week: when Anna Coote was appointed, a young reporter called Glen Owen from The Times had the cheek to call me to ask for the low-down on Coote. I told him to go and tell Peter Stothard, his editor, to get stuffed. But even so, just before I put the phone down, the man begged, "Couldn't you just tell me who Anna Coote lives with?" Now which newly- appointed male political adviser gets that treatment?

Labour basks in its female-friendly post-electoral glow. All those women MPs - and Cherie Booth, too. But already there are dark mutterings about the maleness inside the lads' bunker. The key No 10 Policy Unit has 10 men and one woman, and Downing Street has its own all-boys' football team. When the froth on the cappuccino has blown away, there will have to be real hard benefits for women in all this.