Physical bullying is worst in female-only classrooms, with the problem getting worse as children get older, according to the study. More girls and boys taught in a single-sex environment reported abuse from other pupils compared to the 90 per cent of pupils who attend co-educational schools.

By the age of 16, pupils at all-girls’ schools are “significantly” more likely to be the victim of violent bullying than those at mixed or boys- only schools, researchers at the National Centre for Social Research found.

The study says bullying is “more prevalent in single-sex schools . There are different kinds of pupil dynamics in single-sex schools that lend themselves to a greater risk of bullying overall,” it says.

“Overall, girls in all-girls’ schools were more likely to report being bullied than girls in mixed schools at the ages of 14 and 16, and boys in all-boys’ schools were more likely to report being bullied than boys in mixed schools at the ages of 15 and 16.

“All-girls’ schools in particular may be very different environments from mixed schools in terms of bullying, and there are different risks in these schools that are related to different types of bullying and at different ages when compared to mixed schools.”

The study also found that pupils attending schools where higher proportions of children receive free school meals are less likely to report being bullied, and especially unlikely to report name calling.

But pupils attending schools with higher numbers of children with SEN were more likely to report being bullied and especially likely to report being called names. The researchers found that being from a poorer home does not make children more likely to be bullied.

“An increased likelihood of bullying for pupils in schools with more pupils with SEN is of some concern, and may indicate that more attention needs to be paid to these pupils as potential victims,” the report said.

“It may also indicate that these young people are potential perpetrators of bullying.”

Jill Berry, head of the single-sex Dame Alice Harpur School in Bedford, said: “I don’t agree that girls’ schools have problems with physical bullying. Girls are more subtle - they just exclude each other.

“They are also more likely to report bullying because they are more interested in relationships - friendships are hugely important and girls are much more sensitive. At single-sex schools we have the advantage of focusing anti-bullying strategies much more specifically at one gender.”

Schools minister Nick Gibb has called on teachers at all schools to do more to tackle bullying.

“Over the past five years, I have visited nearly 300 schools around the country. I have been to schools in very affluent areas where behaviour is a real problem because the processes and policies for dealing with bullying are simply not sufficient.”

The researchers interviewed 15,500 children for the report.

NO RARITY VALUE: HOW HALF OF CHILDREN SUFFER

- Half of all children say they have been bullied at school at some point in their lives, and one in five say they have been bullied elsewhere.

- Half of those who are bullied said it had happened in the last year and one in five said it had occurred within the past month.

- For about two-fifths of the children and young people who say they were bullied in school in the last year, the bullying occurred regularly (at least weekly).

- About one-third of those who say that they were bullied outside school in the last year say this occurred regularly (weekly or more).

- Three in five children say their school deals well with bullying.

Source: Department for Education Tellus Survey of 253,755 children.

• Original headline: Girls’ schools revealed as biggest breeding ground for bullies