Social media companies could be forced to exclude young teens from algorithms to make content less addictive for under-16s, under a new bill with heavyweight backing from Labour, Conservatives and child protection experts.

The safer phones bill, a private member's bill from a Labour MP that has high priority in parliament, will be discussed by ministers this week.

It would also commit the government to a review of the sale of phones to teens, including a review of whether additional technological safeguards should be on phones sold to under-16s.

Josh MacAlister, the Labour MP behind the bill, will meet Peter Kyle, the technology secretary, this week to discuss potential government backing for measures in the bill.

Ministers are believed to be open-minded about some of the provisions in the bill and whether any can be applied as the Online Safety Act comes into force - though there is a strong view in government that there should be no ban on sale of phones to teenagers.

The bill is backed by the former Conservative education secretary Kit Malthouse and the new chair of the education select committee, Helen Hayes.

MacAlister, the MP for Whitehaven and Workington, will introduce his bill on Wednesday and will receive a second reading in January. Though private members' bills rarely pass in their original form, MacAlister's was fifth on the ballot, giving it more parliamentary time. Measures in the bills are regularly adopted by the government if there is widespread backing.

Before becoming an MP, MacAlister founded Frontline, a graduate social worker training programme, and previously led the independent review of children's social care.

He said: "The evidence is mounting that children doomscrolling for hours a day is causing widespread harm. We need the equivalent of the 'seatbelt' legislation for social media use for children.

"Parents are in an impossible bind over whether to ostracise their child from social media or expose them to the harms and addiction of content. Countries around the world are now taking bold action and our children risk being left behind."

Keir Starmer, the prime minister, has said he is against "simply banning" mobile phones for under-16s as some campaigners have suggested but said there was a "serious question" to be asked about what they should be allowed to access.

"All parents and everybody across the country is concerned about what can actually be accessed on a phone," he said in July.

Kyle has said previously that he is not convinced by the argument for stronger regulation of phones in schools, saying headteachers are already taking action.

But he also told the Sun: "There's nothing I take off the table when it comes to keeping children, women and girls safe in our society. I'm looking at the international evidence."

The Online Safety Act passed by the previous government has some provisions that place duties on online platforms to protect children's safety but these are not yet fully in force. Ofcom, the communications regulator, is in the process of producing guidance.

The new bill's main provisions include raising the age of internet adulthood from 13 to 16, which would change the age at which companies can get data consent from children without parental permission, a measure aimed at making it harder for companies to push addictive content to children by using their data.

It would make bans in schools a legal requirement by putting the existing guidance on a statutory footing. It would also give Ofcom a specific mandate to protect children's interests, and would commit to a review about the sale of mobile phones to under-16s and how the technology could be adapted to keep teens safer.

Malthouse said there was growing evidence of the impact of smartphones on children that was "deeply alarming". He added: "Being clear about our expectations from providers and regulators and their duties towards our children has to be a step in the right direction."

The children's commissioner for England, Dame Rachel de Souza, and her predecessor Anne Longfield have also given their backing to the bill, as has the National Education Union. The former children's minister Claire Coutinho has also said recently that she hoped the government would go further in regulating children's smartphone use.

A government spokesperson said there were no plans as yet to back legislation for a ban on phones in schools.

"The Online Safety Act will introduce strong safeguards for children, preventing them from accessing harmful and age-inappropriate content," they said. "The vast majority of schools already handle the use of mobile phones effectively, including with bans. Legislating for an outright ban would simply remove the autonomy from school leaders who know their pupils and their communities best."

MacAlister introduced his bill as a group of charities warned Starmer his government could be putting lives at risk if it does not expose smaller websites to the toughest scrutiny possible under new online safety laws.

Charities including the Samaritans, Mind and the Molly Rose Foundation urged No 10 to designate websites promoting disorderly eating or suicide as "category 1" sites that are subject to enhanced scrutiny by Ofcom.

However, the regulator has recommended that such sites do not receive category 1 status and has instead established dedicated supervision teams to manage "small but risky" services.