One in five girls do no physical activity at all, twice the proportion of boys, the research suggests.
Ms Fraser says other research suggests that more than 80% of senior women business leaders played organised sports while growing up.
She says similar high proportions of female executives believe sport made them more disciplined, resilient and competitive in their careers.
She cites the example of former US Secretary of State Condoleezza Rice, once a competitive figure skater and tennis player, while the head of the International Monetary Fund, Christine Lagarde, was in the French national synchronized swimming team.
Ms Fraser says Olympic medallists like Jessica Ennis, Katherine Grainger and Nicola Adams are excellent role models for young women but says women's sport needs better funding and more media coverage.
"I think sport and exercise are ways in which women can reclaim their bodies from the kind of obsessions of the tabloid press and celebrity magazines", says Ms Fraser.
Valerie Dunsford, head of Sheffield High School, part of GDST, said it was important to offer a large range of sports to attract different types of girls.
"Not everyone wants to be out on the hockey pitch", said Ms Dunsford.
"You don't have to be a fantastic sportswoman to bounce on a trampoline and it gives you a great workout."
She said the great sporting advantage of girls schools was a lack of self-consciousness.
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