Katy Ricks is a rare breed among heads of mixed-sex independent schools: she is a woman.
Just 5 per cent of headteachers at mixed secondaries that belong to the largest independent schools' organisation are women, according to a study of the Independent Schools Yearbook. And no private boys' school belonging to the Headmasters' and Headmistresses' Conference has a female head.
The survey shows that among all private girls' schools, including members of other private school bodies, the proportion of female heads rises to 80 per cent. It also found that many of them are unmarried.
Surprisingly, those women who buck the trend in private mixed schools tended to have had their children in their 20s and early 30s, according to the study by Margaret McLay and Marie Brown at Manchester and Manchester Metropolitan universities.
Jenny Watson, deputy chair of the Equal Opportunities Commission, said:
"The small number of female headteachers in co-educational independent schools is, unfortunately, an example of a wider picture.
"This means that tremendous talent is being wasted. Modern recruitment practices mean the 'old boys network' should become a thing of the past."
Ms Ricks, who is the first woman to run Sevenoaks school in Kent, said: "I don't feel I've got any evidence of being discriminated against. I always took the view that I never expected to be treated differently.
"When I was at school at Camden school for girls, it was a given that there was no question that you couldn't do something just because you're a woman."
Part of her success in breaking into the co-educational sector, which is dominated by former boys' schools, came from luck, she said. Her second teaching job was at a boys' independent school in Birmingham, where she had moved after her husband, a university lecturer, secured a research job.
The experience accustomed her to working in a male-dominated environment.
There were just three female teachers in a staff of 130, and the school had a separate staffroom for older teachers, in effect excluding the women.
But women working in state schools are not much better off. While more than two-thirds of England's state-school teachers are women, only 57 per cent of the 21,000 headteachers in the sector are female.
Last month, a parliamentary answer given by David Miliband, former schools minister, revealed 18 local authorities in which male heads outnumber female ones.
The "glass ceiling" appears strongest in Nottinghamshire, where only 170 of 390 heads are women, whereas in Camden, north London, 50 of the authority's 60 heads are women.
In Dr McLay's survey of 79 private schools and interviews with nine women heads, only a few said they had suffered discrimination.
Dr McLay said the result was not surprising as these heads were the ones who had succeeded.
"It's a very 'conservative-with-a-small-c' system in that its tradition is its strength," she said. "But it could be a problem for people who are trying to break the mould."
She said demographic issues and a large number of heads retiring soon would force independent schools to recruit more women leaders.
Her study found that most women heads are older than their male counterparts when first appointed, often because they have taken time out to have children, and that few had the chance to head more than one school, which limited their opportunities.