Female head teachers in England's secondary schools will remain an under-represented group for a quarter of a century, a study has found.
The research notes that there has been an increase in the overall proportion of female head teachers between 2001 and 2015, from 25% to 38%.
But it finds the proportion of women heads is unlikely to match that of women classroom teachers for 25 years.
The University of Nottingham study says the issue is one of social justice.
It says the proportion of female leaders is too low given that women account for the majority of teachers in England's secondary schools at 64%.
The report assessed the number of female heads in post in state secondary schools in England, including free schools and academies, in the academic year 2015-16.
It found only seven local authorities had a proportion of female secondary head teachers that matched that of women secondary teachers nationally.
These were Thurrock, Richmond-Upon-Thames, Merton, Bristol, Bracknell Forest, Wokingham and Darlington.
The study also found that while women were "relatively well-represented in site-based leadership" in academies run by large chains, the majority of chief executive officers were men.
It says: "In the 21st Century, women's under-representation in headship is a matter of social injustice, with women's lack of parity of participation resulting in lack of recognition for their capacity for leadership and from lack of resources with which to achieve it.
"Women are not a minority. A social justice argument suggests women should be represented in headship in the same proportion as their representation in society and/or in the secondary school teaching workforce."
It concludes: "At this rate women's representation in headship will not match their representation in the teaching workforce before 2040."
Report author Dr Kay Fuller, associate professor of educational leadership at Nottingham University, said schools should be setting a good example to young people.
"Girls and boys need to see women influencing decision-making and leading schools equally with men in this important stage of their personal development and learning."
Women should be enabled to negotiate "complex and interacting factors that create barriers to their career advancement", Dr Fuller said.
"Women's careers are interrupted and disrupted disproportionately to men's," she added.
David Simmonds, chairman of the Local Government Association and of the National Employers' Organisation for School Teachers, said: "Local authorities value a diverse workforce and encourage and promote equality in all staffing decisions.
"However, even in maintained schools it is the governing body that decides who to appoint as its head teacher."