The prime minister was facing a major backbench rebellion as around 50 of his MPs put their names to an amendment to the Online Safety Bill.

The amendment called for tougher punishments for tech chiefs who fail to block children from seeing damaging content on their platforms.

A source close to Culture Secretary Michelle Donelan told Sky News she had reached a deal with rebels after talks over the weekend, allowing the prime minister to avoid an embarrassing defeat in the Commons.

The source suggested she liked the intention of the amendment, but the wording "wasn't quite right".

And shortly before the bill was due to be debated, Ms Donelan issued a written statement, confirming the bill would be amended so that senior managers who "have consented or connived in ignoring enforceable requirements, risking serious harm to children" face criminal penalties.

She added: "The criminal penalties, including imprisonment and fines, will be commensurate with similar offences.

"While this amendment will not affect those who have acted in good faith to comply in a proportionate way, it gives the act additional teeth to deliver change and ensure that people are held to account if they fail to properly protect children."

The move to appease the rebels marks the third time Mr Sunak has backed down in the face of uprisings on his backbenches since entering Number 10 in October, having ditched onshore wind farms and planning reforms intended to boost housebuilding.

Former cabinet ministers, including ex-home secretary Priti Patel and former Conservative leader Sir Iain Duncan Smith, are among those backing the change to the Online Safety Bill.

With Labour supporting it too, failure to find a compromise would have seen Mr Sunak on course for his first major defeat in the Commons.

Earlier, a government source told Sky News: "Michelle's main priority has always been strengthening the protections for children online, whilst ensuring adults have more choice and control over what they see.

"She has been clear from the beginning that any additions to the Online Safety Bill need to work in practice and that she would take a pragmatic and common sense approach prioritising children.

"She is pleased that colleagues will no longer be pushing their amendments to a vote following constructive conversation and work."

In its current form, the new internet safety law would require tech companies to remove illegal material from their platforms, with a particular emphasis on protecting children from seeing harmful content.

Social media platforms and other user-generated, content-based sites that break the rules would face large fines from the sector's new regulator, Ofcom.

But the proposed law would only have held tech bosses liable for failing to give information to the watchdog.

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Current protection 'weak'

Sir Iain Duncan Smith had said the proposed protection offered by the draft legislation was "weak" and children needed greater safeguards against seeing "extreme pornography" and material about suicide.

Lucy Powell, the shadow culture secretary, said that Labour want the regulator to have "sufficient teeth" to make Silicon Valley bosses "sit up and take notice".

The NSPCC has been helping drive a campaign to have managers made criminally responsible for failing to offer protection to youngsters.

Richard Collard, associate head of child safety online policy at the children's charity, said: "By committing to senior manager liability, the culture secretary has sent a strong and welcome signal that she will give the Online Safety Bill the teeth needed to drive a culture change within the heart of tech companies that will help protect children from future tragedies.

"The government has rightly listened to the concerns raised by MPs and we look forward to working with ministers to ensure the final legislation holds senior managers accountable in practice if their products continue to put children at risk of preventable harm and sexual abuse."

Ian Russell, the father of schoolgirl Molly Russell, who died by self-harm while suffering "negative effects of online content", said the threat of imprisonment is "the only thing" that will make the bosses "put safety near the top of their agenda".

"I think that's a really important thing in terms of changing the corporate culture at these platforms," he told BBC Newsnight.