"I do believe in quotas." So said Jude Kelly, artistic director of the Southbank Centre, on Wednesday evening (13 February 2013) at a talk organised by global children's charity Plan UK. The event was one of a series of talks by women for women aimed at helping girls to fulfil their potential.

In the run-up to the Southbank Centre's Women of the World Festival (WOW), Kelly was there to talk about how she has come to where she is today, the challenges she has faced and the people who have influenced her along the way. The director touched upon a lot of issues, including education, self-development and mentoring, but informing the whole discussion was the fight for gender equality.

The quota remark came in response to a question I asked about how gender equality is to be achieved in the arts. Earlier in the evening Kelly had mentioned that WOW has created a climate at the Southbank Centre in which discussions of gender were part of programming, something that wasn't the case before the launch of the festival in 2011. She also described particular events - such as the speed-mentoring sessions the centre ran on the London Eye in October 2012 to celebrate the first ever International Day of the Girl - seeking to give girls the confidence to pursue careers they hadn't previously considered.

But such steps, she said, are not enough if real change is to occur: "There can be no trickle-down". Instead, we must seek to change the power structures that are standing in the way of gender equality. Orchestras, she pointed out, used to be majority male, until they began auditioning people behind a screen so the person's playing was the only thing being assessed. Now the balance is better.

If we are to achieve gender equality in other areas of the arts - playwriting, for example, and, as a consequence of that, the representation of women on stage and screen - something similar is required. If women are not advancing in the arts at the rate they should be, we need to take steps to address that situation.

Kelly stressed that making space for women to succeed "is not about pushing men out"; it's rather about "persuading them that it'll be better for everyone if they make room". I suspect that men working in the arts need less persuading on this count than those in many other professions, but it's undoubtedly true - as Kelly remarked - that the fight for gender equality cannot be won without the involvement and support of enlightened menfolk. WOW is an inclusive event, rather than being women-only, for precisely this reason.

Alongside affirmative action, however, another crucial element in changing the status quo is helping women to transform the way they think about themselves. Because we've been taught that women and girls are supposed to be docile, that ambition is a negative attribute, that it's more important to be liked than to succeed, we're putting up barriers to our own progress.

This is certainly the case in arts administration, a field in which women outnumber men at low and mid-level jobs but disappear the higher up the ladder you go. Partly this is to do with the family-unfriendly nature of these industries causing women to drop out of the race when they have children, but it's also to do with the fact that society tells women that striving for the top is unladylike.

This then has a knock-on effect for girls and young women lower down the ladder, who have their socially ingrained notion of the rightful place of women in the workplace confirmed.

That's not to say, of course, that there are no women in positions of power in the arts in this country. Kelly remarked that when she was studying drama at the University of Birmingham there were hardly any female directors for her to look up to. That certainly isn't the case today. But the situation is far from equal. As Kelly said on Wednesday evening, we mustn't be complacent. Pessimism doesn't help anyone, but neither does blind optimism in the face of ugly truths.

Sign the Plan UK petition asking the UN to make girls' education a priority.

- By Jo Caird