A woman in a tight top with scarlet toenails peeping out of dangerously high heels sounds just the sort of sidekick Gordon Brown needs. What better deputy leader to spice up his granite demeanour than a photogenic mum of three – especially one with a serious CV and a nice southern English accent to counter his gruff Scots brogue?

The only hitch is that the lady pitching for a high-profile new role on Team Gordon is no bright-eyed political ingenue but Harriet Harman – one of the party’s most enduring figures, who has spent decades campaigning for women’s rights. And while there’s no doubting her polished appearance, like most women of her age, the would-be new deputy leader of the Labour party has a past.

Over the years new Labour’s high command has fallen in and out of love with Harman, who has sometimes tested their affections to the limit. “Crap”, “desperate” and “bloody incompetent” are just some of the words certain colleagues privately use to describe her.

Today, however, it appears Harman is once again the party darling, after securing the second highest number of nominations from MPs last week in the deputy leadership contest. To some surprise at Westminster, she is now just behind Alan Johnson, the man once regarded as runaway favourite.

Not bad for a candidate who has repeatedly been written off by her detractors, and through her marriage to Jack Dromey, Labour’s treasurer, who blew the whistle on dodgy loans to the party, is closely associated with the cash for honours affair.

“People may be nasty about me, but 65 MPs have nominated me as deputy leader. That’s more than any other candidate except one. So perhaps others have got even more people bad-mouthing them,” she says.

An aide arrives at her Westminster office to report “amazing” news: “Gwyneth” has just signed up to the Harman campaign. That’s Dunwoody, not Paltrow – the long-est-serving female member of parliament and a formidable old battleaxe. Other backers include Yvette Cooper, wife of Brown’s closest adviser Ed Balls; Douglas Alexander, the transport secretary; and Alistair Darling, the trade and industry secretary – all such arch Brownites that rival candidates for the deputy leadership mutter darkly that Harriet must be “Gordon’s choice”.

Not so says Harman: “Gordon isn’t endorsing anyone. He can’t.” But she believes they’d make the best team. She describes herself as “Radio 2” to Brown’s “Radio 4”.

“People are saying to me, at the next general election, we want you and Gordon campaigning on our high street. You two will give us the best chance of winning.”

If she pulls it off, it will be an extraordinary comeback for the MP for Camberwell and Peckham. It’s years since she has been in cabinet – she was sacked after only 15 months as social security secretary in 1998 following high-profile disputes with fellow minister Frank Field and backbench anger over the cuts she made to benefits for single mothers – and has a knack of upsetting people.

Though it was long ago, many Labour voters have never forgiven her for eschewing bog-standard comprehensives and choosing to send her children to selective schools instead. (She went to St Paul’s girls’ school, one of the country’s top private schools.) One went to the prestigious Roman Catholic Oratory in west London (along with the junior Blairs); another was educated at a Church of England school; while the youngest went to St Olave’s grammar school in Orpington, Kent – a long way from Harman’s deprived south London constituency.

The debate over education and selective schools is back at the top of the political agenda, after the Tories last week dropped their long-standing support for grammar schools. Harman, who is now minister of state for justice, has had plenty of time to reflect on her own canny use of the system, which triggered uproar when it emerged in 1996. So it is surprising to find that she is not better rehearsed when asked if she now regrets the choices she made.

She says she has “nothing to add” to a letter she posted on her website about it months ago, which says that her children never went to private schools, and that she fully supports comprehensive education (just not for her own children, obviously).

“I really haven’t got anything more to say,” she sighs.

I know that Harman was deeply anxious about this skeleton in her closet when she launched her deputy leadership campaign last autumn – so perhaps her defensiveness stems more from a desperate desire to move on than any pretence that it’s no big deal. But the issue won’t go away.

Earlier this year it emerged that Ruth Kelly, the former education secretary, sent her special needs son to a private boarding school. What did Harman make of that?

“I am not going to comment on issues in relation to a child which I don’t know, who was entitled to his privacy. I made that very clear at the time,” she says testily.

She may want to close the subject down, but I press her on whether it is okay for politicians to preach one thing in public and practise another in private. After all, such dilemmas go to the heart of what it means to be a government minister.

“I would simply say that parents will make er, er, er, choices for their children, and politicians are accountable,” she replies falteringly. “We’ve got a policy for free education, and that’s what we’re in government to do. Parents have got to make their own decisions. No government actually dictates to any parent what choice they should make. Parents make their own choices, whether they are politicians or not.”

This sounds like carte blanche for government ministers to do exactly as they please for their own families, whatever their public policy.

Where does she draw the line – private health insurance? Apparently that’s okay too.

“It’s not for, you know, the government shouldn’t be dictating. I can’t really go any further than that. What the government does is decide on policy and try to make sure there are good hospitals and schools. That’s what the remit of government is.”

Given her bitter experience of being labelled a hypocrite, and her lawyer’s training, it’s strange that she will not, or cannot, articulate her position better. It will be seized on by critics as evidence that she’s just not up to the job of deputy leader.

But that might be to misunderstand the nature of the role. It now seems highly unlikely that the winning candidate will follow in John Prescott’s footsteps and become deputy prime minister. They will certainly not be running a Whitehall department. This means the job will be largely symbolic – and that could be Harman’s selling point.

Her campaign doesn’t pretend to be based on complex policy proposals, but on the simplest of arguments – that she is a woman, whose background and image will help make Brown more electable in the south.

“The parliamentary party has really warmed to the idea that a team of a man and a woman is a better team. People now know we’ve got an agenda for women in this country, as well as men. So the first stage of my mission is 100% accomplished.”

Many voters appear to agree she is the best foil to Brown. In a YouGov poll of 2,000 people earlier this month, 14% said electing Harman as deputy would make them more likely to back Labour at the next general election, beating Hilary Benn and Peter Hain into second place (both on 10%). None of the other candidates got out of single figures.

Her key themes have been promoting flexible working for mothers, supporting women forced to stay at home to care for elderly parents or sick youngsters, and promoting youth services.

It’s a lot of hard graft for a job that won’t come with the perks Prescott has enjoyed. If she wins, it’s unlikely she’ll enjoy the stately home, Dorneywood, where Prescott infamously played croquet.

But after cash for honours, Brown and his team will be anxious to show they are not just in it for themselves – and Harman, more than others, is painfully aware of the loss of public trust in her party. Her own husband dramatically raised the stakes in the cash for honours affair when he revealed in March last year that neither he nor any other elected official had been told about secret loans to Labour.

One can only imagine the conversation at the Harman-Dromey breakfast table before he dropped his bombshell. “The party needed to know whether their treasurer knew about it, and the treasurer needed to make it clear to the party he didn’t. Once it was in the public domain, it was important for him to make it clear what the position was. It was difficult, but I don’t think there was any alternative for him.”

Despite her impressive list of nominations, Harman’s bid for the deputy leadership is far from in the bag. The voting process is complicated, and the contest is still regarded as wide open. But win or lose, she will soon be back in the cabinet. Her supporters hope she will make less of a hash of it this time.

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