The NUT said female teachers were told they were “not hard enough” to be heads. In a submission to ministers, it accused the Government of developing a school leadership culture that discriminated against women. It said one teacher had been told she was too nice, too kind, too thoughtful and supportive to be a head.

“Vague notions of personal suitability for leadership can sometimes work to the disadvantage of women,” the union said.

Ed Balls, the Children, Schools and Families Secretary, told Parliament this week that he would proceed with the School Teachers’ Review Body recommendations to restructure school leaders’ pay and responsibilities. But the NUT has warned that its exclusion from talks would jeopardise ministers’ plans.

The reforms include extending the pay scale beyond pound;150,000 to cover “superheads” and others responsible for two or more schools.

The union, which took its members out on strike over pay last month, has threatened legal action against ministers in the past for not including it in talks about schools.

Its submission to ministers provoked mixed responses. Anne Swift, a Scarborough infant school head, said some governing bodies looked for a “tough” head to sort things out when they would be better off finding someone with more female attributes.

“A lot of women don’t come across as aggressive and macho, but are very courageous in holding fast to their principles,” she said.

But Ann Holland, a Gloucestershire primary head, said courage and decisiveness were attributes found as often in female leaders as male, and that traditionally female attributes such as communication were increasingly valued.

The Department for Children, Schools and Families denied any discrimination. “Like parents, we simply want the best people for the job,” a spokesman said. “We see no reason why women would not be just as qualified as men.”