A ban on mobile phones in schools in England is to be introduced by the government to ensure that “critical safeguarding legislation” is passed.

The government will table an amendment to the children’s wellbeing and schools bill in the House of Lords after the bill was held up by peers on opposition benches.

It will make existing guidance on mobile phone bans in schools statutory, a move that ministers have resisted until now.

The government had consistently argued that the vast majority of schools had already banned mobile phones, and that there was no need to add a legal requirement. They finally capitulated, however, describing it as “a pragmatic measure” to get the bill through.

Announcing the move on Monday, the education minister Jacqui Smith told the Lords: “We recognise the strength of feeling on this issue, both in this house and beyond.”

“Notwithstanding the fact that we think the guidance we already have in place provides headteachers and schools with a range of approaches to be able to deliver the objective that we all share, we are committing to tabling an amendment in lieu which will place the existing guidance on a statutory footing on the face of the bill, creating a clear legal requirement for schools.”

“We’ve listened to concerns about how we support headteachers in delivering on this policy and we have listened to parliament.”

The bill is regarded by many as the biggest piece of child protection legislation in decades and includes proposals for a compulsory register for children who are not in school, a crackdown on profiteering in children’s social care, and a “single unique identifier” to help agencies track a child’s welfare.

Pepe Di’Iasio, the general secretary of the Association of School and College Leaders, said: “A statutory ban on mobile phones in schools doesn’t really change very much. Most schools already have policies in place under which pupils are not permitted to use mobile phones.

“What would really be helpful is for the government to make funding available to schools for the safe and secure storage of mobile phones, such as storage lockers or locked pouches.”

The education secretary, Bridget Phillipson, has previously written to headteachers in England to stress that schools should be phone-free throughout the entire school day, but the guidance has been non-statutory.

Research from the children’s commissioner for England last year found that 99.8% of primary schools and 90% of secondary schools already had policies in place that limited or restricted the use of mobile phones during the school day.

However, many headteachers, dealing with challenges from parents, will welcome the move, which will provide clarity in classrooms.

Ministers have only grudgingly agreed to it. A government spokesperson said: “The repeated attempts by the Conservatives and Liberal Democrats to kill off some of the most far-reaching child protection legislation is utterly abhorrent, and a dismal failure of some of the most vulnerable children in our country.

“After more than a decade where children’s social care and the system of child safeguarding was left to rot by these parties in office, and that saw horrific child abuse cases such as those of Arthur Labinjo-Hughes, Star Hobson and Sara Sharif, this government moved quickly to fix what was broken – only to be thwarted at every turn by unelected opposition peers.

“The blocking of measures in this legislation, which includes direct manifesto commitments, such as the introduction of free breakfast clubs and limits to branded school uniform, saving families hundreds of pounds, by unelected Conservative and Liberal Democrat peers is a complete affront to democracy.”

A Department for Education spokesperson said: “We have been consistently clear that mobile phones have no place in schools, and the majority already prohibit them. This amendment makes existing guidance statutory, giving legal force to what schools are already doing in practice.”

A Liberal Democrat spokesperson said: “We promised to put children’s wellbeing before party politics, and by dragging the government kicking and screaming to adopt our mobile phone ban in schools, the Liberal Democrats have delivered a major win for pupils, teachers, and families.

“Now the government must ensure all schools have the necessary support and funding to manage this transition, so that every classroom can be a smartphone-free zone.”

Paul Whiteman, the general secretary of the National Association of Head Teachers, said: “Statutory guidance will give school leaders the clarity they need to implement a ban, and will remove any ambiguity or differences between how schools approach smartphone policies.”