An inquiry should be set up to look into allegations of a “rape culture” at a number of independent schools, a senior MP has said.

Writing in the Sunday Telegraph, Robert Halfon said that what has allegedly been happening at some of the country’s most distinguished schools was “appalling” and it had spread to state schools too.

The chair of the Education Select Committee said that countless stories had emerged of female pupils being “objectified, harassed and sexually assaulted”, with websites set up by students highlighting “a rape culture”.

Mr Halfon said senior staff had been “at best unable or at worst unwilling” to deal with what had gone on.

He welcomed an investigation by the Metropolitan Police but said an independent inquiry should be launched after the police probe.

Mr Halfon added: “After the police investigation, there should be an independent inquiry looking into all these allegations – what exactly has gone on, why it was allowed to take place and what the schools did to try and stop it.

“Rather than marking their own safeguarding failures (as some schools are trying to do by appointing their own judge and jury), headteachers and governors should be held directly accountable.

“If found wanting, they should step down from their positions.”

His comments come after Scotland Yard said it has received multiple reports of offences after reviewing a website featuring anonymous submissions of “misogyny, harassment, abuse and assault”.

The force said it has reviewed testimonies on the Everyone’s Invited website, a site where people can anonymously share their experiences of abuse.

It said officers have been establishing whether any potential victims in London could be encouraged to report crimes, with several people coming forward.

A link is also now available on the website to directly report crimes to Scotland Yard.

It comes after a number of independent schools in the country have been accused of failing to deal with complaints about a “rape culture”, with many testimonies shared on Everyone’s Invited.

Highgate School, a north London private school, announced it would be launching an independent review into issues raised.

A school spokesperson said: “We are horrified and deeply shocked by the testimonies on ‘Everyone’s Invited’ and elsewhere.

“The governing body have appointed The Rt Hon Dame Anne Rafferty to lead the independent review into the issues raised by the testimonies.”

Mr Halfon said that Ofsted should be responsible for safeguarding inspection of private schools and they must fund a national helpline so female students can report incidents confidentially and get help and advice.

He added: “Given that it looks that safeguarding has fallen short, there should be a fundamental review of school safeguarding and just one body responsible for safeguarding inspection of private schools – Ofsted – rather than the current system, which allows the independent sector to have its own inspection regime.

“There must be a national helpline, funded by these schools, to ensure that when such abuse takes place female students in particular can report confidentially and get advice and assistance.

“The schools have to be required to provide mental health and wellbeing counsellors, to give support for present and past pupils affected by these awful revelations.”

The Metropolitan Police said where schools had been named on the website, officers have been making contact with them to offer specialist support to any potential victims.

Scotland Yard’s rape and sexual offences lead Detective Superintendent Mel Laremore said more than 100 schools are cited on the “Everyone’s Invited” website.

She told BBC Radio 4’s Today programme on Saturday it is a “national issue”, adding: “I think it’s more widespread than private schools. I think we’re still looking into the exact scope of how wide this is spread but certainly I know there’s already over 100 schools cited on the website which do reach out to national parameters.

“The private school element of this is a factor, in that certainly for us as the Metropolitan Police we have a safer schools officers and a safer schools network, we have identified ourselves that there isn’t a safer schools network within the private schools.”

A Government spokesperson said: “We are very concerned by the significant number of allegations recently posted on the ‘Everyone’s Invited’ website. The abuse of children and young people in all its forms is abhorrent.

“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.”