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Keir Starmer has ramped up the pressure on ministers to reopen schools as soon as possible, warning that the longer they remain closed the more damage will be done to poorer pupils’ life chances.

As Starmer urged the government to come up with a timeframe for its “exit strategy” from the Covid-19 lockdown, his spokesperson said the Labour leader feared disadvantaged children would fall further behind their peers.

“We are concerned that the longer the schools are shut the bigger the inequalities between those children that have access to good homeschooling versus those who may not have access to good homeschooling, because of overcrowded accommodation [for example],” the spokesperson said.

“There are extraordinary lengths that teachers and parents are going to during these very difficult times. Where we want to see is clarity from the government about how it is going to maintain education during the lockdown and what support is going to be made available.”

Education secretary Gavin Williamson told MPs on Wednesday that schools would reopen in a “phased manner”, but he refused to give any timelines apart from saying that there were no plans to keep them open during the summer holidays.

Starmer’s intervention follows warnings from current and former Ofsted chiefs that online schoolwork is causing even bigger divides between pupils from different backgrounds and is a “very poor substitute” for classroom teaching.

The Education Endowment Foundation (EEF) charity this week published an analysis suggesting that the coronavirus pandemic in the UK risked “reversing” all the gains made in narrowing the attainment gap over the past decade.

The loss of several weeks of classroom schooling, which could amount to a full term, is hitting poorer households disproportionately because of a lack of home wifi, computer equipment, household space and parental skills or supervision.

The spring and summer terms for children in their penultimate year before GCSEs and A-levels are particularly crucial in their learning, but they face the disruption to a sixth of their entire curriculum across all subjects.

The Sutton Trust estimates that while 30% of middle class pupils are taking part in online lessons every day, that figure drops to just 16% for poorer pupils. In the country’s most deprived areas, teachers report that up to 30% of their pupils simply don’t have internet access or the technology needed.

The Department for Education has in recent days unveiled plans to give children from disadvantaged background across England free laptops, tablets and 4G routers, but many think even that is no replacement for classroom tuition.

On Tuesday, Ofsted chief Amanda Spielman told the BBC’s Newsnight: “It’s not just the poorest, it’s the ones with little English… with special educational needs, the young ones who can’t read and write yet.”

And earlier this week, she told the education select committee: “We have to accept that what can be done while schools are substantially closed is a very poor substitute for full normal education.

“And it would be unrealistic for anyone, including me, to expect the vast majority of children to have made the same progress they would have made if they’d been in school, which is why I truly believe that it’s in children’s interests to be back in school as early as possible.”

Her predecessor Sir Michael Wilshaw said that unless schools after the lockdown are open for weekends or longer days and even holidays, some children would have to repeat a whole year to catch up. “That will have huge logistical differences and progression problems for university.”

Some countries are already reopening their schools across Europe, with different years going back at different times.