The leader of England’s top public schools says she is willing to refer boys to the police after more than 3,000 allegations, ranging from sexual harassment to rape, were posted on Instagram.

Eton, St Paul’s, Harrow, Hampton and Latymer Upper are named in the anonymous accounts of sexual abuse, some from girls as young as 11, posted on @everyonesinvited.

A small number of state schools and universities are also named on the site, set up by Soma Sara, 22, a former boarder at Wycombe Abbey.

The claims include more than 50 of rape, 35 allegedly linked to schools.

One contributor describes being choked until she passed out. Others detail Instagram pages where nude photographs are shared and rated. Many describe being pressured into giving oral sex. One said she was told by boys that she reminded them of “the Asian girls in porn”.

Maria Miller, the former chairwoman of the women and equalities committee, said this weekend that schools and the police “should not ignore rape or violent sexual assault [just] because they involve children” and “boys must be taught trying to strangle someone is not normal”.

In a letter to alumni, Sally-Anne Huang, the first female high master of St Paul’s and head of the Headmasters’ and Headmistresses’ Conference, which represents top public schools, said she had seen the Instagram site, “which seeks to bring people together to understand and reject sexual violence and harassment”.

She wrote: “There are many responses to its testimonials section, some harrowing, and there is a focus on rape culture within schools. A number of these testimonials cite Paulines as the perpetrators … We have made children’s services aware of the website and would always investigate fully … informing the police where a criminal act may have been committed.”

No names had been provided and so the police had not been informed, Huang added.

Sarah Fletcher, head of St Paul’s girls’ school, wrote to parents last week about comments by its pupils on the website. “It is evident that there remains a culture among some young men and boys of this activity … My heart goes out to everyone whose experiences are recorded,” she said, adding that counselling would be offered.

Kevin Knibbs, headmaster at Hampton School in southwest London, wrote to parents: “We have no tolerance whatsoever of the kind of behaviours highlighted on this website.”

Many public schools emphasised that they had brought in initiatives, including Good Lad workshops, to tackle toxic masculine behaviour.

But in an interview with The Times yesterday, Sara said: “In the holidays I grew up in London social circles and sex was a palpable presence throughout my teens. Disgusting behaviour was trivialised. It could be sexual coercion, rape, catcalling, sexual bullying, stealthing [non-consensual condom removal], image-based abuse, victim blaming. Sexual abuse didn’t just exist. It thrived. It was rife.”

Miller, who led an inquiry into sexual abuse in schools five years ago, said too many were still not reporting abuse to the police or doing enough to stop teenagers posting intimate photos online.

“No one wants to criminalise young people, but if there have been violent sexual attacks on young women in schools this cannot be ignored,” she said.

A former pupil at St Paul’s girls’ school said: “The school could have done much more. Sexual violence and consent were discussed with boys at the boys’ school in the form of a joint feminist society, even though this was often met with laughter or disdain by male students.”

A leading former headmaster said schools should report boys to the police in the hope that it would stop them getting a criminal record later. He also warned girls that a nude photo texted to a boy would end up online. “Don’t trust boys,” he said. Parents should protect their sons from online pornography, which was distorting their behaviour, and schools should “get the police to explain what the law says”, he added. “Boys need to worry.”

Barnaby Lenon, chairman of the Independent Schools Council and former headmaster of Harrow, said many schools had introduced courses on “how to treat girls properly”, which, he added, “would never have happened 20 years ago”.