Strict bans on mobile phones in schools have “close to zero” impact on student learning and show no evidence of improvements in attendance or online bullying, a study has found.

Researchers at US universities including Stanford and Duke looked at nearly 1,800 US schools where students’ phones were kept in locked pouches and found little or no differences in outcomes compared with similar schools without strict bans.

The report concluded that among schools instituting a ban: “For academic achievement, average effects on test scores are consistently close to zero.”

The results will come as a disappointment to teaching unions and campaigners in England who backed the government’s recent move to restrict the use of mobile phones in schools. A ban is likely to come into force next year.

But Prof Thomas Dee of Stanford University’s graduate school of education, one of the report’s authors, said it would be wrong for policymakers to see the results as a reason to shy away from restrictions.

“One of the concerns I have about this study is that it might encourage people to walk away from phone bans as a compelling reform. And I think that would be a major mistake,” Dee told NPR.

“There are some encouraging results in the midst of these mixed findings. They are driving down phone usage, and as schools have longer experiences with phone bans, we’re seeing a shift towards more positive outcomes.”

The study, published by the National Bureau of Economic Research, concentrated on secondary schools that required students to place their phones in magnetic pouches and found a substantial fall in phone activity by the third year of a ban based on GPS data analysed by the researchers.

But lower phone use did not translate into measurable improvements in student attainment or other non-academic outcomes.

“Average effects on standardized test scores are close to zero and precisely estimated, with similarly small and null effects on attendance, classroom attention, and perceived online bullying,” the researchers concluded, including relatively small “modest positive effects” on maths scores among older students and negative effects on younger pupils.

It also found a spike in suspensions and a dip in students’ feelings of wellbeing in the first year after a ban as schools adapted to the change. “Over time, however, disciplinary impacts fade and wellbeing rebounds, becoming positive in subsequent years,” the report said.

Last month, the UK’s Department for Education announced that it would legislate to make restrictions on phones a statutory requirement for England’s state schools. Recent research by England’s children’s commissioner found that more than 90% of schools already had policies barring the use of phones but the new rules are likely to toughen those policies by requiring phones be handed in or locked away during the school day.

The Girls’ Day Schools Trust, which runs 25 private and state schools, has announced a ban on phones for pupils up to year 11 from September, citing the harmful effects on girls in particular.

Philip Purvis, the trust’s director of education, said: “There is a growing body of research showing the potential harms of mobile phones and social media use, along with recent large-scale studies highlighting the specific impact on teenage girls, from addiction to poor mental health and wellbeing.”

As the A-level and GCSE season approaches, England’s exam regulator has warned students not to take phones or smart watches into exam halls after more than 500 candidates were disqualified last year.

Ian Bauckham, the chief regulator of Ofqual, said: “Being found with a smart device during an exam can have serious consequences, including loss of marks or disqualification from the subject. Do not become one of those statistics and risk your qualification and your future prospects. Keep your phone out of the exam hall.”