Speaking at the annual conference of the Girls’ Day School Trust, chief executive Helen Fraser, 63, stressed girls should be “ambitious” when hunting down a suitor, and learn to find a man that would help around the home, and be a “cheerleader” for their career.

Girls can have it all, said Fraser, who was the former managing director of Penguin Books. A career, marriage and motherhood could be achieved with the right partner.

Without the right husband, Fraser said women risk not hitting the “glass ceiling”, but confronting a “nappy wall”, by having to choose between children and a career.

“Just as I believe we should always encourage our girls to aspire to the best universities, I believe we should encourage our girls to be ambitious in their relationships,” she said.

Fraser said she takes inspiration from Sheryl Sandberg, the chief operating officer of Facebook, who once said “The most important career choice you make is who you marry.”

“Is this what we should be making space for our girls to learn?” she suggested.

“That if you want children and a career, a partner who shares the load at home really, really matters?

“Or a partner who cares as much about you succeeding in your career as they does about their own – and is a cheerleader for you through your triumphs and setbacks.

“Is it about teaching girls to find partners who will make space for their own careers in a relationship?”

Fraser oversees 24 independent schools and two academies in her job, and has two daughters and two stepdaughters, only taking six weeks’ full maternity leave after the birth of her children.

She said GCSEs should be limited for the sake of broadening life skills.

She said: “And looking back at the history of women in the 140 years of the GDST’s history, should we be teaching girls to push back the walls of inequality even further – to make the world a fairer place for all women?”

She also said there was a danger that we are being “infantilised” by new technology and that we’re in danger of losing sight of the truth that some learning is more of a “slow casserole, with knowledge stewing in our minds to form a richer, deeper flavour”.

“So I’m a firm believer in the importance for our students of switching off the computer, the radio, the smartphone, the TV, and any other distractions, and reading a whole book,” she said.

“When you read a book, you are in contact with another mind – probably wiser and more informed than you. With the internet, you are in contact with dry facts.”