The amendment has backing from Baroness Benjamin, the Liberal Democrat peer and former children’s TV presenter; Conservative former education minister Lord Nash; the Labour peer Baroness Berger and Baroness Cass, an independent member of the House of Lords, who is a paediatrician.
Separately, the Liberal Democrats have tabled an amendment which would introduce film-style age ratings, meaning some social media platforms would be restricted based on the type of content they were hosting.
The letter from Labour MPs, which includes the signatures of a number of committee chairs and former frontbenchers, said many constituents had contacted the MPs to express concerns about the effects of social media on young people.
It read: “Across our constituencies, we hear the same message: children are anxious, unhappy and unable to focus on learning. They are not building the social skills needed to thrive, nor having the experience that will prepare them for adulthood.”
The MPs said that “around the world, government are recognising the severity of the crisis and taking action”, noting Australia’s ban and that “Denmark, France, Norway, New Zealand and Greece are expected to follow suit.
The UK “risks being left behind” on the issue, they wrote.
The letter, external, thought to be organised by Plymouth Moor View MP Fred Thomas, was signed by education select committee chair Helen Hayes, former whip Vicky Foxcroft, former education minister Catherine McKinnell, and former shadow cabinet minister Richard Burgon, among others.
It is the latest example of political pressure on the government to propose a social media ban.
Last week, Conservative leader Kemi Badenoch said she would introduce an under-16s ban if her party won the next election.
Under the Liberal Democrats’ plan, platforms using addictive algorithmic feeds or hosting “inappropriate content” would be restricted to users aged over 16, while sites with “graphic violence or pornography” would become adult-only.
Speaking to BBC Breakfast, Lib Dem leader Sir Ed Davey described his approach as “a ban but a more sophisticated ban”.
He said it would ensure “the best approach to make sure the benefits of the internet can be enjoyed by our children but they can be fully protected from the addictive harm of some of these social media platforms”.