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“My agenda has been a bit vanguardist, but that’s the way we want to go,” she says. “It’s a fierce agenda and not always consensual. But I believe the strong economies of the future will be the ones that turn their back on the old boys’ network.”

Not that she is likely to wheel out the pink glasses for her occasional appearances deputising at prime minister’s questions. During these sessions she prefers some more conservative tortoiseshell ones — perhaps they have brought her luck, too, as she defied all predictions that she would be a disaster at the dispatch box. Indeed, to widespread surprise, she was a success, handling most tricky questions with aplomb, shooting off funny, feisty one-liners: “All the commentators said I would fall flat on my face. Actually, I was glad to prove them wrong.”

Does she enjoy going into combat? She pauses for a long time. Well — it’s bad when it goes wrong. She has gaffed, memorably telling the House of Commons that “Fred the Shred” was knighted for charity work, not services to banking. A few hours later she was forced to issue a correction.

“Ummm, errr, yeah, I do enjoy it, actually,” she says, eventually. “I’m basically putting forward to the House the agenda that Gordon and the rest of the cabinet have collectively agreed. I agree with that agenda so strongly, I’m happy to put it forward. To have the chance in the House of Commons to stand up for what I believe in is a great opportunity.”

An opportunity, too, to bang the drum for women’s issues? “As deputy leader I am now, more than I’ve ever been before, in a position to do something about the issues which previously have not had a voice,” she says. “We have come in from the outside, we’ve come of age. We’re in from the cold.”

Indeed, she is ready to take the fight to the next level, enthusing about a recent meeting with Nancy Pelosi, the first female Speaker of the US House of Representatives. Harman wants to set up an international summit for women leaders to take place alongside the male-dominated G20 meeting of world leaders and which would be called the “Gender 20”. She is excited that female political leaders today feel less obliged than their predecessors to pretend they are men.

“Margaret Thatcher used to be the only role model, but she’s not a role model for today’s generation of female leaders,” she says. “Thatcher was like: I can do it as well as men, I can do it on men’s terms. Now it is about women doing it because they are women, not despite it.”

Will Brown pay much attention to any of this talk? Probably not. Indeed, the prime minister seems to have a bit of a problem with his women MPs, some of whom meet up for dinner to moan about him. They have been dubbed Wags: Women Against Gordon. In June, Caroline Flint, the former Europe minister, accused him of using women ministers as “window dressing”.

If Harman sympathises with this line, she’s too smart to say. “I can always understand anyone’s frustration about being a woman in a man’s world,” she says diplomatically.

Still, her unflinching determination to promote the interests of women will no doubt go down well with female voters, as will her ability to defend her beliefs. She recently faced — and fought off — resistance from Peter Mandelson, the business secretary, over her Equality Bill. He warned that the new anti-discrimination measures could be a dangerous burden on businesses struggling with the recession, but Harman refused to back down, winning the day by claiming businesses that treat women, the disabled and other minorities properly get better results.

One suspects Brown didn’t dare risk her wrath by derailing this most important of projects. After all, he is relying on her readiness to fight as Labour embarks on a desperate battle for re-election in the next few months. The party may — as of Friday — be trailing 14 points behind the Tories, with a poll last week predicting a majority of more than 150 for David Cameron, but Harman’s got her fingers in her ears.

“I don’t accept what we are told by the Tories, which is that they’ve won the next election,” she says. “I think that’s arrogance. I don’t accept that the election is already lost.”

With less than a year to go, the Whitehall machine is clearly reluctant to crank into action for any but the most pressing policy initiatives, but Harman denies that mandarins are twiddling their thumbs while they wait for the new regime. The way she sees it, the government is absolutely bursting with energy and ideas.

“I don’t accept the argument we’re now just in limbo at all. It’s the very opposite,” she puffs, rattling off a list of the most pressing issues in the government’s in-box: Afghanistan, tackling the recession, sorting out the mess over expenses.

The ship may be sinking, but the eternally optimistic Harman won’t be down for long.

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