Britain's madrassas have faced more than 400 allegations of physical abuse in the past three years, a BBC investigation has discovered.
But only a tiny number have led to successful prosecutions.
The revelation has led to calls for formal regulation of the schools, attended by more than 250,000 Muslim children every day for Koran lessons.
The chairman of the Mosques and Imams National Advisory Board said he would treat the issue as a matter of urgency.
Leading Muslim figures said families often faced pressure not to go to court or even to make a formal complaint.
A senior prosecutor told the BBC its figures were likely to represent the tip of an iceberg.
BBC Radio 4's File on 4 asked more than 200 local authorities in England, Scotland and Wales how many allegations of physical and sexual abuse had come to light in the past three years.
One hundred and ninety-one of them agreed to provide information, disclosing a total of 421 cases of physical abuse. But only 10 of those cases went to court, and the BBC was only able to identify two that led to convictions.
The councils also disclosed 30 allegations of sexual abuse in the Islamic supplementary schools over the past three years, which led to four prosecutions but only one conviction.
The offender in that case was Mohammed Hanif Khan, an imam from Stoke-on-Trent who was imprisoned for 16 years in March this year for raping a 12-year-old boy and sexually assaulting a 15-year-old.
Some local authorities said community pressure had led families to withdraw complaints.
In one physical abuse case in Lambeth, two members of staff at a mosque allegedly attacked children with pencils and a phone cable - but the victims later refused to take the case further.
In Lancashire, police added that children as young as six had reported being punched in the back, slapped, kicked and having their hair pulled.
In several cases, pupils said they were hit with sticks or other implements.
The number of cases appeared to be rising - among those councils which broke down the figures by year, there were 89 allegations of physical abuse in 2009, 178 in 2010 and 146 in the first nine months of this year.
With more than half of Britain's 2.5m-strong Muslim population aged 25 or under, the number of madrassas, where children spend about 10 hours each week learning to recite the Koran in Arabic, is also growing rapidly.
Mohammad Shahid Raza, chairman of the Mosques and Imams National Advisory Board, set up by Muslim organisations to improve standards in mosques, said he would now treat the issue as a matter of urgency.
"These figures are very, very alarming and shocking. There is no justification for such punishments within our mosque schools," he said.
"I'm not sure how wide this unacceptable practice is, but our responsibility is to make those who run the mosques realise we live in a civilised society and this is not acceptable at any cost."
Mr Raza said he wanted the issue dealt with through self-regulation, but there are calls for the government to take action.
Dr Ghayasuddin Siddiqui, founder of the Muslim Institute think tank, said large numbers of unregulated organisations were opening madrassas across the country - most in mosques but some in garages, abandoned pubs or private homes.
Abuse was far too common, he said.
"We are basically destroying the lives of young people," he said. "Some kind of system must be put in place to ensure that only teaching takes place there, not sexual or physical abuse."
Nazir Afzal, the chief crown prosecutor for the North West of England, said he believed the BBC's figures represented "a significant underestimate".
"We have a duty to ensure that people feel confident about coming forward," he said.
"If there is one victim there will be more, and therefore it is essential for victims to come forward, for parents to support them and for criminal justice practitioners to take these incidents seriously."
Corporal punishment is legal in religious settings, so long as it does not exceed "reasonable chastisement".
An official report published last year which called for a legal ban on the practice - and which was accepted by the Labour government just before the general election - has not yet led to any action.
The report's author, Sir Roger Singleton, chair of the Independent Safeguard Authority, said the BBC's figures were worrying and should be investigated further:
"That does lend weight to my view that we're not just dealing with isolated instances," he said. "So I would be quite concerned to understand why the allegations have not resulted in a greater number of prosecutions."
The children's minister, Tim Loughton, declined to be interviewed. But in a statement, the Department for Education said Mr Loughton had met Sir Roger and was considering his recommendations.
"The government does not support the use of physical punishment in schools and other children's settings," it said.