According to the UK culture minister, modifying the internet safety law to empower regulators to bring legal action against social media executives who are found to have failed to protect children’s safety is something she “is not ruling out.”

According to Michele Donelan, who spoke to the BBC on Friday, she would adopt a “sensible approach” to the modifications required by numerous Conservative MPs.

Her remarks come a day after Downing Street announced it was taking into account ideas supported by 36 Conservative MPs that could result in executives serving up to two years in prison for breaking the law.

Priti Patel, a former home secretary, and Iain Duncan Smith, a former labour and pensions minister, are among the MPs who have signed the amendment.

Additionally announcing on Friday that it would support the amendment, Labour added to the pressure on the prime minister to budge.

“Labour has been asking for criminal accountability for individuals who manage these corporations throughout the passage of the bill, and we will join forces across the house to improve it in this way,” said Lucy Powell, the shadow culture secretary.

If the amendment is passed, Ofcom, the communications watchdog, would have the authority to bring legal action against social media company leaders who are found to have broken the law. After U-turns on planning and onshore wind farms, if ministers incorporate it in the law, it will be the third instance in which Prime Minister Rishi Sunak has acceded to the requests of his backbenchers.

On Thursday, a representative of Downing Street said, “Our goal is to hold social media platforms accountable for damaging information, while also ensuring that the UK remains a fantastic environment to invest in and grow a tech firm. We are sure we can accomplish both of these goals. When the report stage is through, we will carefully analyze each of the proposed changes to the online safety bill and state our stance.

According to the Daily Telegraph, one concession being considered by ministers would assign specific senior employees at tech companies responsibility for certain aspects of online safety, such as reporting child sexual exploitation material to the National Crime Agency or being held accountable for “repeated and systemic” violations of the law.

The bill, which aims to impose stricter regulations on a variety of online materials that ministers believe are seriously harming users, was partly influenced by Frances Haugen’s testimony, a former Facebook employee who claimed the company repeatedly put profits before user safety.

Companies will be required by the law to remove any content that encourages self-harm, shows sexual violence, or aids in suicide. Companies will also be forced to set and enforce tight age restrictions as well as provide evaluations of the hazards their platforms represent to children.

As it stands, the measure provides Ofcom the authority to penalise businesses up to 10% of their annual global revenue for breaking the law. Executives will only be subject to prosecution by Ofcom if they refuse to comply with an investigation. However, this has angered a lot of Conservative MPs who think the regulator needs stronger authority.

The amendment, which has the support of 37 MPs overall, would let Ofcom to bring charges against specific executives if it could be shown that they had helped violate the law’s provisions meant to ensure the safety of minors. The maximum prison term the judges might inflict is two years.

The NSPCC has welcomed the change and demanded that “leadership management takes responsibility for our children’s safety.”

The amendment has the support of Molly Russell’s father, a 14-year-old who committed suicide in 2017 after viewing damaging content about self-harm and suicide on social media.

“At Molly’s inquest, the world witnessed the scope of the profoundly upsetting material she was exposed to as a young kid suffering from mental illness,” Ian Russell said. The role that social media played in her death has yet to be acknowledged by anyone.

“The chance to prevent this from happening again and to direct tech executives’ attention to the need to ensure that their platforms are safe online environments for children to be is provided by including senior manager responsibility in the online safety law.

“I implore the culture secretary and the prime minister to embrace this critical modification to the draft legislation, listen to activists and a rising number of their own MPs,” she said.

Other modifications to the bill include changing earlier proposals to address damaging content viewed by adults that does not meet the level of criminality, including as cyberbullying and sexist and racist material. The bill will undergo report and third reading in the House of Commons next week.

Tech companies will have to be explicit about how they would censor such information in their terms and conditions. When using social media platforms, users will also have the choice of asking to have this content blocked.