When Titilola Dawudu was 16, an older woman took her out to the theatre for the first time. Dawudu put on an appropriately big, puffy dress and stepped into an alien world. “I was fascinated. I fell in love with the theatre world then.”

That woman was Lucy Neal, co-founder of the London International Festival of Theatre. She was Dawudu’s first mentor, involved in a scheme at Dawudu’s school. Neal would instil in her a belief in the importance of mentors for those who are underrepresented in the arts, which, as a black woman from a working class family, she exemplified.

Dawudu is now a successful playwright and theatre director working at Ovalhouse theatre in London. She credits Neal and the mentors she met as a student in dramatic writing at Central Saint Martins college in London with enabling her to launch her career. “Mentoring isn’t offered much in universities,” she says. “It needs to be, because sometimes for women of colour, or with disabilities, the door might be shut in your face.”

A helping hand can make all the difference to women in the arts. There is a greater proportion of women studying and training in the arts than working in the industry – and the gap is widest at the top. A report published by the Freelands Foundation last year showed that although 63% of creative arts students in 2016 were female, just under a third of artists represented by London’s major galleries were women. Similar underrepresentation is apparent in the film industry: the Fawcett Society reported that in 2017, only 16.4% of film directors and 30.9% of film producers were women.

The British Theatre Consortium, meanwhile, said that in 2013, just 31% of new plays were written by women – despite the fact that the latest figures show that 70% of drama students are female.

This is where the University Women in the Arts campaign is stepping in. The scheme aims to build the next generation of female leaders in the arts by connecting 15 female students with successful women each year. It also runs events to help arts students build a bridge between their studies and work. Jennifer Tuckett, the campaign founder and a dramatic writing lecturer at Central Saint Martins, recalls how Dawudu came to her tutorial crying, telling her that her mentorship changed her life. “There’s a real gap when you finish a course: nobody’s helping you get into the industry,” she says. “A lot of female arts students drop off at that stage.”

The project has inspired Tuckett to begin a PhD on the topic at the University of Cambridge. She hopes her research will inform government policy addressing gender inequality in the arts industry. Her initial findings suggest that confidence is one of the main barriers for female students – and one that is poorly understood by all-male management teams. “Our mentors have spoken about resilience – you get a setback and something goes wrong, so you think, that’s me; I’d better go and do something else. It’s about understanding that you have to keep going,” she says.

Mentees also reported that their universities didn’t teach them industry skills, including how to write applications and gain work experience – or how to find an agent. “For a long time I felt that it was aliens from another planet who worked in the arts,” says Tuckett. “I think if I’d had classes at university explaining how the arts work and what the different roles were, it would have helped so much.”

There is a more serious barrier facing women in the arts industries, highlighted by the #MeToo campaign following the Harvey Weinstein sexual harassment scandal. Tuckett is collaborating with the thinktank GenPol on a set of guidelines for students, teachers and lecturers on how to spot and deal with gender-based abuse, bullying and violence in the arts.

These guidelines will look at the ways women in the arts tend to be limited in their roles. “When we go to a museum, a movie or the theatre, we’re presented with tons of work authored by men, produced by men, and with plenty of women’s bodies,” explains Lilia Giugni, chief executive of GenPol. “There’s objectification and sexualisation of women, without much recognition of the fantastic work women artists do at all levels.”

Vanessa Brady, founder of the Society of British and International Interior Design, says it’s not uncommon for her to work on a design project where there are 15 people leading – yet she’s the only woman. “Men will be front of the queue for everything,” she says. “They’ll be the first to grab the mic at an event, while women stand back. Women need to be much more engaging about their skills and abilities – they don’t promote themselves as much as men.”

Without female leaders, ambitious young women feel they don’t belong, says Vanessa Reed, chief executive of the PRS Foundation, which runs a fund for new women songwriters. “Artists we’ve supported say that it is alienating to young, talented women to see that the recording studio backstage crew is mostly male – and that most senior roles in the music industry seem to be taken up by men.”

Reed says targeted initiatives are important for supporting women who lack confidence to apply for funds. “We asked women who applied to our Women Make Music fund why they didn’t apply to another [of our funds], and they said: ‘I didn’t think I would have a chance’.”

For Dawudu, the first step to help female arts students into the industry – and stay there – is for women to help each other. She’s now mentoring and supporting drama students herself.

“The gatekeepers and decision-makers are the old boys who hang around together. There’s this affinity bias; people hire or programme work for people like them,” she says. “As women, we need to support each other more, raise each other up – and know that there’s room for us all.”

• University Women in the Arts is looking for female arts students to submit work inspired by their views and experiences of abuse, bullying and harassment, in the arts or more generally, for an upcoming book. Full details here.