As prime minister of New Zealand, Helen Clark brushed off criticism of her sex. Could she become the first woman to run the United Nations?

In the course of a political career that has lasted over 30 years, Helen Clark only thought of quitting once. With a personal poll rating of just 2% soon after becoming party leader in 1993, she asked a few close friends whether there was any point continuing. "They said, 'You've just got to keep standing there', which was the best advice. If you keep standing, actually very few will come after you."

Clark went on to become New Zealand's first elected female prime minister in 1999 – leading for three consecutive terms – and is now the most powerful woman at the United Nations, working her second term as head of the UN development programme. She could well become the first woman to lead the organisation once the incumbent Ban Ki-Moon stands down in a few years.

En route to Davos, the alpine schmoozefest for powerbrokers, Clark was in London last week to deliver a lecture on leadership for the Women of the Year organisation. With so few female heads of state to act as a yardstick, she has been compared to Margaret Thatcher, despite her vastly different Labour party politics and incredibly impressive, no-nonsense support of other women.

On the advice from close friends to keep on as party leader, she persisted. "They said: 'Don't give in.' It's not in my nature to give in anyway." She lambasts organisers at Davos for failing to increase the number of women and, on panels, happily discusses female representation in the same breath as her views on Syria or other affairs of state.

By the end of her nine years as prime minister in 2008, New Zealand's governor general, cabinet secretary, attorney general and speaker were all women. Meanwhile, opponents in her last unsuccessful election urged voters to "ditch the bitch".

Now 63, there can be few women better qualified to talk about the treatment of women in power. Clark decided early on to ignore much of the criticism of her sex, she says. "There was a lot of very gender-based criticism. You know, 'Your voice is too low, your teeth are too crooked'. They don't like your hairstyle, they don't like your clothes. In fact, they don't really like anything about you, and maybe this all adds up to [the notion] that they don't really like a woman doing what you're doing.

"But, you know, if you found all that hurtful then you're probably not going to be able to survive these jobs. You have to be able to dismiss it, and I seem to have developed a style, where [journalists] always knew that I'd get to a point and say 'move on', you know, 'get over it'."

But was she really not that bothered by patronising remarks? "Earlier on, it annoyed me, but then I got to the point in my career where I said: 'Look, who cares, it's irrelevant and if I comment on it, it's an issue, so let's move on.' I've got bigger things to do."

Given this attitude, her view of Julia Gillard, the former prime minister of Australia whose speech denouncing misogynists in parliament was a YouTube sensation, is less surprising. "Many women around the world saw this as incredible, but how did it play in Australia?" Clark asks. Gillard was, of course, subsequently ousted as leader of the Australian Labor party .

"I had no personal experience of it," Clark says of sexual harassment, "but, if there is one silver lining from all this, we need all these people coming forward ... Women are not prepared to suffer in silence. The lid is off and that has to be healthy."

She is also well aware of the double standards that mark a woman in power, pointing out the fact that "strength" in men is described as "toughness" in women and judged accordingly. But pondering why men are more likely to push themselves forward, she suggests that more women than men "want to balance a range of factors" when getting to the top. One of the biggest factors is childbirth.

Elected to parliament at 31, she has remained childless by choice. "It just would have been totally impractical without a spouse who was prepared to completely give up a career," she says. Her husband, sociologist Peter Davis, was on a fast-track university career, so she felt that wasn't an option. Asked if she ever regretted the decision, she says: "No, definitely not … It was absolutely right for me."

But women who want to combine motherhood with powerful positions should be able to, she says. "It really points to the need for a lot more discussion of families and of the role of boys and girls, women and men, so that the boys grow up with an expectation to be an equal in the household."

Clark was brought up on a farm in rural New Zealand, and her own mother gave up her career as a teacher as soon as she married. Clark, who kept her maiden name, never wanted to go down the same route. There's "some truth", she says, in the story that she cried on her wedding day. So why did she get married? "It was 1981. It wasn't that usual for people in public life [to be unmarried]. It still isn't." She doesn't seem to mind that this makes her marriage sound like political expediency – she is still happily married to the same man 34 years later.

She first became interested in politics because of international affairs – the death of JFK when she was a teenager, the war in Vietnam and the injustices of apartheid. Now her name is potentially in the frame for the top job at the UN, the first woman to lead the diverse group of 193 nations.

The election of a UN secretary-general is a process so complicated it takes years to go through, all of it behind closed doors. Clark has many points in her favour, not least her current job and the fact that New Zealand is part of the amusingly named Weog group (Western Europe and Other Group, but essentially it means the old developed countries). There hasn't been a secretary-general from Weog since Kurt Waldheim in the 1970s, which in the obtuse nature of UN affairs could mean it's about time another one got the job.

Asked if she wants the job, she refects on how being a woman would play out in that role. "There will be interest in whether the UN will have a first woman because they're looking like the last bastions, as it were." But it could also be a massive "turn-off" to others, she admits. She loves her job, she says, and laughs when I point out she hasn't answered my question. "If there's enough support for the style of leadership that I have, it will be interesting."

Back in New Zealand, there are fewer women in government than there were when she was prime minister. At the recent Davos meeting, only 15% of delegates were women, an even smaller number than last year. "These battles never go away," she says. "It shouldn't just depend on a group of exceptionally ambitious women. We need it to be in the culture of our societies, institutionalising it in the normal scheme of things. [Then] there will be a lot of women at the top."