The Government refused to give a timeline for the end of lockdown, with Gavin Williamson, the Education Secretary, saying he cannot give a date for schools to reopen.

His remarks followed speculation that a three-phase plan to lift the lockdown could see schools reopen as early as in three weeks’ time.

Mr Williamson has announced a package of measures aimed at supporting children’s learning at home, amid concerns that the most vulnerable will fall behind.

Disadvantaged children – including those who have been in care and those with a social worker – will be given free laptops and tablets to ensure they do not miss out on learning from home.

Youngsters who do not have mobile or broadband internet will also be given 4G routers, and major telecommunications providers have pledged to temporarily exempt education sites from data charges.

A Government-backed "virtual school" will launch on Monday, with free online daily lesson plans for children aged four to 15. Since schools closed on March 20, just 34 per cent of pupils have taken part in live or recorded online lessons, according to the poll by the Sutton Trust, a social mobility charity, and Public First, a political research agency.

At private schools, 51 per cent of primary and 57 per cent of secondary students have accessed online lessons every day, compared to just 19 per cent of state primary and 22 per cent of state secondary students.

The survey, which asked 1,500 parents and 6,500 teachers a range of questions about children's online learning provisions, also found disparities in the amount of work that children are completing.

Fifty per cent of teachers in private schools said they are receiving more than three quarters of work back, compared with 27 per cent in the best state schools and just eight per cent in the least advantaged state schools.

Ministers have come under pressure to announce a timeline on schools reopening, which is seen by some as holding the key to ending lockdown since it would enable parents to go back to work. But Mr Williamson's remarks at the Government daily press briefing indicated that there are no plans for schools to reopen ahead of the easing of lockdown more generally.

He said schools will not return until the Government's five tests for lifting lockdown are met. Announced by the Prime Minister's stand-in, Dominic Raab, when he confirmed that the lockdown would be extended, the tests include the death rate consistently falling, that the NHS's ability to cope has been protected and that any changes do not risk a second peak.