More than 8,000 allegations have now been made by school pupils on a website gathering testimonies of sexual violence and abuse.
"Rape culture" was a problem for all schools, said Soma Sara, founder of the Everyone's Invited website.
Many of the perpetrators are claimed to be at the same school or in the same social groups.
Norfolk Chief Constable Simon Bailey blamed the "volume of pornographic material that's being consumed".
"There's an erosion of an understanding of what normal sexual relationships look like," said the National Police Chiefs' Council lead on child protection.
'Normalising' sexual violence
"We have a real problem here," he told BBC News, saying that a police helpline would be set up and promising to "investigate those allegations which are of a criminal nature".
The helpline will "ensure victims can access advice and support where needed", said the Prime Minister's official spokesman.
On Twitter, the Education Secretary for England, Gavin Williamson, said: "No school - whether an independent school or state school - should ever be an environment where young people feel unsafe, let alone somewhere that sexual abuse can take place."
"The allegations that I have heard in recent days are shocking and abhorrent."
Mr Williamson said "any victim of these sickening acts" should raise their concerns with someone they trust, such as a teacher, family member or the police. "We will take appropriate action," he wrote on Twitter.
Robert Halfon, chairman of the House of Commons education select committee, called for a "full independent inquiry to find out why so many female students have suffered from sexual abuse and harassment".
Highgate School, among the private schools caught up in the claims, says it is launching an "immediate external review of the sexual abuse and harassment allegations" and is "working on an anti-sexism plan".
Dulwich College's head teacher Joe Spence said: "The behaviour described is distressing and entirely unacceptable" and "we are meeting with victims to listen to their experiences and their concerns, and we will act on them".
The website Everyone's Invited was set up last year as a place where victims can post anonymous accounts of abuse they had suffered.
Many of the accounts describe allegations of sexual harassment and sexual violence carried out against young women by young men who are at school or college or university with them, or part of the same social groups.
"These are stories of rape culture - so where behaviour that's not normal is normalised," Ms Sara told the BBC.
"Sexual harassment, groping at a Christmas party, image-based abuse, revenge porn, non-consensual sharing of intimate photos - and just general sexism and misogyny," she said, describing the experiences being raised.
Ms Sara said "normalising and trivialising" such incidents could create a "gateway to more extreme criminal acts, such as rape and sexual assault".
The website initially drew attention to private schools, particularly in London, but the 22-year-old said that was a consequence of her own background - and that the range of testimonies, from state and private schools, showed this was a much wider issue.
"Rape culture is a universal problem - it's everywhere, in all schools, all universities and all of society," she told BBC News.
Anonymous testimonies listed on the site do not reveal the identity of the pupils or their attackers, but many schools are named. Many of the incidents recounted took place outside school or university premises.
Paul Whiteman, leader of the National Association of Head Teachers said school leaders had to "ask ourselves what more we can all do to prevent sexual harassment and violence" - but he said "this is a problem that reaches far beyond the school gates".
'Call out' behaviour
Chief Constable Bailey warned that pornography was distorting how some young people saw relationships - and that this had become a "driver" of the type of behaviour being reported online.
Ms Sara agreed with this, and said the most effective response would be for young people themselves to confront such attitudes.
"It's really important we encourage our children and teenagers to be empowered to stand up to their friends and call out this behaviour, because I think that's the most influential space."
Labour leader Sir Keir Starmer said: "There's got to be an inquiry and it has got to get going very fast, this is serious."
He also called for "cultural change in terms of behaviour in our schools and in our young people, but also in the respect that is shown particularly for women and girls".
The Department for Education said it was very concerned by the allegations posted on Everyone's Invited.
A spokeswoman said: "The vast majority of schools, colleges and universities take their safeguarding responsibilities very seriously, so it is particularly shocking when allegations of abuse are made in connection with a place of education, where everyone should feel secure and be protected.
"Working together, the Department for Education, the Home Office and the National Police Chiefs' Council are in contact with Everyone's Invited to provide support, protection and advice to those who are reporting abuse, including on contacting professionals or the police if they wish."