Department for Education (DfE) guidance already says phones shouldn't be allowed, but head teachers are able to ignore it if they disagree.
An amendment to the Children's Wellbeing and Schools Bill now proposes making it a legal requirement.
Teachers have long voiced concerns that smartphones distract pupils and can add to problems such as bullying.
"We have been consistently clear that mobile phones have no place in schools, and the majority already prohibit them," said a DfE spokesperson.
"This amendment makes existing guidance statutory, giving legal force to what schools are already doing in practice."
On Monday, the House of Lords voted by a majority of 107 to ban phones during the school day.
The proposal, by shadow education minister Baroness Barran, includes a potential exception for sixth-formers, medical devices and some boarding school settings.
The House of Commons is now expected to vote on the amendment on Wednesday.
The NASUWT union previously said it supported a statutory ban, while headteachers' union the NAHT also backs it.
NAHT general secretary Paul Whiteman said it would give "clarity" and "remove any ambiguity or differences between how schools approach smartphone policies".
"Schools will only then need to decide how to implement and enforce a ban across their school community and the government must provide any support they require to do so effectively," added Mr Whiteman.
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Skills minister Baroness Smith of Malvern said the government had listened to parliament and "to concerns about how we support headteachers in delivering on this policy".
However Laura Trott, the shadow education secretary, painted it as a win for the Conservatives.
"I am delighted we have forced Labour to see sense and U-turn," she said ."This is fantastic news for headteachers, parents and pupils across the country."
Valentina Gomez was due to speak at the Unite the Kingdom rally, which is being organised by far-right activist Tommy Robinson, on 16 May, and posted on X that her UK electronic travel authorisation (ETA) had been approved.
But after backlash from MPs and campaigners, the government has excluded the US-based Christian influencer because her presence "would not be conducive to the public good", Sky News understands.
This is the same reason given for Kanye West's permission to travel to the UK to headline the Wireless festival in London being blocked by the government.
West had been heavily criticised in the past for antisemitic remarks.
Ms Gomez shares her anti-Islam views on social media, and has posted a videos of herself burning a Koran with a flamethrower.
The government has discretion to ban foreign nationals from the UK if their presence is not considered "conducive to the public good".
A ban can be ordered by the home secretary personally, and government guidance states it will normally involve serious issues such as national security, war crimes, corruption or extremism.
Sky News understands that in Ms Gomez's case, the government blocked her entry on the grounds that the democratic right to expression does not extend to promoting hatred or extremism.
The 26-year-old influencer attended and spoke at a previous Unite the Kingdom rally, to which between 110,000 and 150,000 people turned up.
She told the told the crowd at the event in September: "If these rapist Muslims take over they will not only rape your women, they will behead your sons."
The Muslim Council of Britain wrote to Home Secretary Shabana Mahmood expressing concern about allowing Ms Gomez to enter the UK, saying to do so would "lead to less safety and security on the streets of Britain".
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The council has welcomed the decision to block her from entering the UK, saying: "People who propagate hate speech and division should not be given free entry to the United Kingdom.
"This decision is the right course of action by the UK government and this should be a precedent for others who chose to promote disinformation and hatred."
Last week, Homelessness charity Centrepoint said it had cut ties with Sharon Osbourne after she expressed support for next month's Unite the Kingdom rally.
He was the face of Granada's hit Zoo Time - a nature series exploring animal behaviour which ran from 1956 to 1967.
Morris also fronted the BBC's Life In The Animal World and other documentaries for the broadcaster after starting his career with the corporation in 1965.
The Wiltshire-born author won global acclaim in 1967 for his most successful book, The Naked Ape: A Zoologist's Study Of The Human Animal.
Many more books followed, including The Human Zoo (1969), Manwatching (1977) and The Naked Man (1977), and he contributed to more than 90 titles during his career.
Morris followed his passion for animals after joining the Army in 1946 and completing two years of national service.
He also served as London Zoo's curator of mammals for eight years from 1959.
He began his academic career studying zoology at the University of Birmingham, and later completed a doctorate in animal behaviour at Oxford University, where he remained to study the reproductive behaviour of birds.
His son Jason said he died on Sunday, but that his father had enjoyed a "lifetime of exploration, curiosity and creativity".
"A zoologist, manwatcher, author and artist, he was still writing and painting right up until his death.
"He was a great man and an even better father and grandfather."
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Half marathon organisers apologise after route too long
Run For All, which operates events across the UK, admitted in a statement that the race "was longer than 13.1 miles".
The organisation offered an apology and explained how the mistake happened.
It said an initial investigation found a turning point was wrongly positioned by more than 250m, which meant the route was longer by over half a kilometre.
Run For All said: "We are disappointed that this has happened and apologise unreservedly that this has occurred and we take full responsibility for the error.
"Our initial investigation shows that the turning point was positioned incorrectly with it being 256m out, which has resulted in the route therefore being 512m long overall."
Runners have been told their results have been updated to provide a time equivalent to a 13.1-mile (21km) finish.
Participants have also been told they will be offered half-price entry to next year's run.
Organisers added they would be "running a full internal investigation... to ensure this doesn't take place again".
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The marathon, which began in the city centre before moving out to the northwest suburbs and looping back, coincided with a 10K run on the same day.
Run For All was created by the late amateur athlete Jane Tomlinson CBE, after her cancer diagnosis.
The company describes itself as a "fundraising vehicle for a huge number of local and national charities".
Michael Stewart, 57, from New Barnet, and Anthony Stewart, 60, from East Finchley, were aged 15 and 18 when they allegedly set upon Anthony Littler in an alleyway as he walked home on 1 May 1984.
The prosecution said the brothers, who have denied murder, were among a group of young males who attacked 45-year-old Mr Littler with blunt weapons in East Finchley.
The victim suffered two skull fractures and a "catastrophic brain injury" from which he died at the scene.
Michael and Anthony Stewart had told police during house-to-house inquiries they were at home at the time of the attack, with Anthony claiming he never used the alley.
The breakthrough came on the 29th anniversary of Mr Littler's death, when the defendants' younger brother Daniel, who was aged 10 at the time, came forward to police following a family falling out.
He told officers they had confessed to the killing and boasted about being involved in "queer bashing", jurors heard.
Years after the killing, Michael Stewart also allegedly admitted his guilt to a girlfriend and even showed her where it happened.
Prosecutor John Price KC told jurors at the Old Bailey in London: "You will hear that this was not the only time that Michael Stewart, Anthony Stewart and others associated with them used violence on a solitary man they did not know, in a public place.
"By the spring of 1984, it is alleged by the prosecution that for quite a while this had been a habit or hobby of theirs.
"They had begun by targeting men whom they thought might be homosexual men."
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In 2022, police reopened the investigation and deployed covert investigative techniques against the brothers, bugging their cars and Michael's home, jurors were told.
The prosecutor said Mr Littler had been a real ale enthusiast and had spent the evening before his death at a pub in Carshalton, Surrey.
After arriving at East Finchley Tube station at 12.18am on 1 May, he was attacked, the court heard.
Immediately after the incident, Michael Stewart allegedly called for an ambulance from a phone box but a search for an injured man was called off after he hung up.
The trial continues.