Teachers and other professionals who do not report child abuse suspicions should face prosecution, the ex-director of public prosecutions says.
Keir Starmer said under a British "mandatory reporting" law, those who failed to act could be sent to jail.
Declassified files uncovered by BBC Panorama show how schools have repeatedly failed to protect children from sex offenders.
But the government said mandatory reporting was not the answer.
While statutory guidance has been issued previously urging professionals such as teachers, doctors and social workers to report child abuse, failure to do so is not a crime in England, Scotland and Wales.
In Northern Ireland, the Criminal Law Act 1967 makes it an offence to fail to disclose an arrestable offence - including those against children - to police.
'Gap in law'
Mr Starmer, who was succeeded as director of public prosecutions by Alison Saunders on Friday, said it was time to "plug a gap in the law" that had been there for a "very, very long time".
"If you're in a position of authority or responsibility in relation to children, and you have cause to believe that a child has been abused, or is about to be abused, you really ought to do something about it," he said.
He said a criminal penalty would "focus people's minds" and said there should be "immunity for individuals if they did report".
He said the penalty for failing to report abuse could be a short jail sentence or a fine.
"There are just too many examples of cases where those who have suspected abuse have not really done anything about it and the perpetrator has either got away with it or, worse still, been able to perpetuate the offending."
He added: "I would have a reasonably broad category of individuals that were subject to the law.
"Obviously school teachers, but others in a position of authority or responsibility in relation to children, including other educational institutions, even sporting institutions."
Similar laws are already in places in countries including the US, Canada and Australia.
For the first time, the Catholic Church and the Church of England have also come out in support of mandatory reporting.
Bishop Paul Butler, head of safeguarding at the Church of England, said: "We have to think of the child first, not ourselves, not the institution, what's best for the child."
But the government has no plans to change the law.
The Department for Education said professionals "should refer immediately to social care when they are concerned about a child".
"This happens every year in many thousands of cases and numbers of referrals have increased over recent years," it added.
"Other countries have tried mandatory reporting and there is no evidence to show that it is a better system for protecting children."
And Dame Clare Tickell, chief executive of the Action for Children, told BBC Radio 4's Today programme: "We are not convinced that making it mandatory will do what we need it to do."
She said the reporting of child abuse in the UK was on the rise and that a "huge issue" was that "teachers and people across the system are not sufficiently trained to see those early signs of abuse".
It was important they knew how to spot those signs "and not to feel that they may be prosecuted if they don't", she added.
But Jonathan West, of the Mandate Now coalition of charities, welcomed Mr Starmer's call, adding that "social services can't actually act on cases they haven't been told about".
He added: "Schools, other organisations, often don't really want to have a child abuse scandal on their hands.
"It is surprisingly common that schools want to handle such things in house."
Ever since the Jimmy Savile revelations, Panorama has been investigating secret historical records and looking at what government officials knew about abuse in children's homes and boarding schools.
Declassified government files going back 60 years show how senior civil servants were well aware that school authorities routinely hid child abuse - preferring instead to protect the reputation of their own institutions - and the law was an inadequate deterrent.
One of the most detailed historical files in the National Archives is about a cover-up at the Royal Alexandra and Albert school.
Today it is a well-regarded state boarding school in Reigate, Surrey.
However, research by Panorama has revealed that seven child abusers worked at the school between the 1950s and the 1980s.
You can watch Panorama: After Savile: No More Secrets, BBC One, Monday 4 November at 20:30 GMT and then available in the UK on the BBC iPlayer.