Tech firms could be subjected to tough new regulations to prevent teenagers being bombarded by targeted advertising and endless notifications, and routinely having their location tracked by GPS.

The new measures to protect the privacy and mental health of children are being proposed by a cross-party campaign that is likely to inflict a defeat on the government within weeks.

An amendment from the crossbencher and film director Lady (Beeban) Kidron to a bill going through the House of Lords has won the support of senior Tories, Labour and the Lib Dems. Its backers say a barrage of information, based on data-gathering, is causing social anxieties, affecting young people’s sleep and poses a risk of personal information being disseminated online.

The amendment to the data protection bill, laid down by Kidron, calls for technology companies to be subject to “minimum standards of age-appropriate design”. She said ministers who are resisting the move should not be “put off by tech lobbyists”.

Sources have told the Observer that the government is likely to face defeat if it fails to offer a concession before a vote scheduled for mid-December. If the amendment is passed, the government would then have to decide whether it is willing to countenance the political headache of attempting to remove it in the Commons.

The push has the backing of the high-profile Conservative peer Dido Harding, the former chief executive of TalkTalk, who told the Observer she had come to the decision with a “heavy heart”: “I’ve spent years in telecoms thinking that competition drives the right outcomes, but it doesn’t appear to be happening. I would love to believe that commercial platforms will move fast enough that you don’t have to regulate, but there is no sign of that.”

“It is difficult to reach consensus when there is no referee in the room. To make sure children are protected, we should set standards.”

Harding added that society did not think twice about setting health and safety standards for children’s toys, or regulating television programmes. “I know the positive power of the digital world – but there are downsides as well as the upsides,” she said, describing how GPS could help people and companies to know children’s location, and how devices made young people vulnerable to bullying 24 hours a day.

“You can’t make people completely safe but you can provide a seatbelt,” she added.

Kidron has argued that the key is preventing the commercial imperatives of large companies being prioritised over the rights and wellbeing of children. She said “eye-watering and inappropriate data-harvesting” being used to profile young people had major implications.

Her amendment suggests age-appropriate design could include: ensuring high privacy settings are switched on by default when a user is under 16; not revealing GPS locations; preventing data from being widely shared; and giving children time off from endless notifications during school and sleep hours. It could also require commercially driven content presented to children to be clearly identified.

Matt Hancock, the digital minister, said the government sympathised with the sentiment behind the amendment but disagreed that it represented the best way forward: “Earlier this year we legislated for a new code of practice for social media companies, and are consulting on our internet safety strategy which will put it into practice,” he said. “We want to keep children safe online, but this particular amendment risks creating confusion about data protection responsibilities.”