The education secretary has confirmed a blanket approach to schools after announcing just days ago that only a select number would remain closed after the Christmas holidays.
Labour said the education secretary's "incompetent" handling of the return of schools had caused "huge stress" to pupils, parents and staff, amid calls for more clarity about the criteria for reopening.
An emergency Cabinet Office meeting was convened on New Year's Day to take the latest decision, which overrules a previous government announcement this week.
The government had initially said 50 education authorities in southern England would have their primary schools closed until at least 18 January, other than to teach vulnerable children and those of key workers.
But several London boroughs with high cases were left off the list, and nine local authority leaders sent a joint letter to Mr Williamson warning that they were prepared to take legal action.
The leaders of the boroughs of Islington, Camden, Hackney, Lambeth, Lewisham, Greenwich, Haringey and Harrow all signed the letter.
Some councils even suggested they were prepared to defy the government and support schools that wanted to close against government advice.
Richard Watts, leader of Islington Council - which was threatened with legal action by the government last month after it proposed switching to online teaching - said it was "unacceptable" that the decision had been taken so late.
Caroline Kerr, the leader of Kingston Council in southwest London, said: "We are dismayed at the way the government has handled this situation and recognise that this has caused a great deal of worry for parents and carers, children, and for teachers and school staff in our borough."
Confirming the news, Mayor of London Sadiq Khan, said: "The government have finally seen sense and U-turned. All primary schools across London will be treated the same.
"This is the right decision - and I want to thank education minister Nick Gibb for our constructive conversations over the past two days."
In a statement on Friday night Mr Williamson said moving further parts of London to remote education "really is a last resort and a temporary solution".
He added: "As infection rates rise across the country, and particularly in London, we must make this move to protect our country and the NHS. We will continue to keep the list of local authorities under review, and reopen classrooms as soon as we possibly can."
The leaders of the boroughs to have written to the government had said they were “struggling to understand the rationale” behind the government’s policy.
Around a million pupils aged between four and 11 will now be learning remotely from Monday, when schools were originally expected to return.
The closures could go beyond 18 January, which is the date Boris Johnson has said the decision to teach children at home will be reviewed.
Tottenham MP David Lammy said the change in policy was "welcome but so utterly predictable".
"It has caused unnecessary anxiety for students, parents and students," he said.
"We cannot continue to be behind the curve like this. If school leaders behaved like this Ofsted would describe them as failing."
Paul Whiteman, general secretary of the National Association of Head Teachers, said: “Just at the moment when we need some decisive leadership, the government is at sixes and sevens.
"There is no clear rationale for why some schools are being closed and others are not and why primaries and special schools are being treated differently to secondaries.
“The government appears to be following neither the science nor the advice of education professionals on how best to preserve the quality of education for young people.
"The government cannot expect to command public confidence with such a confusing and last-minute approach.”
Kate Green, Labour's shadow education secretary, said the move was "yet another government U-turn creating chaos for parents just two days before the start of term".
"Gavin Williamson’s incompetent handling of the return of schools and colleges is creating huge stress for parents, pupils, and school and college staff and damaging children’s education," she said.
“The government failed to get mass testing for schools and colleges in place when Labour called for it and they have failed to develop credible plans for remote learning when pupils cannot be in school.
“This U-turn was needed to provide consistency in London. However, Gavin Williamson must still clarify why some schools in tier 4 are closing and what the criteria for reopening will be. School and college staff urgently need reassurance that the government is putting proper support in place to make all schools Covid secure work environments.”
There have been calls for the government to delay the reopening of schools for the rest of the country, not just for London, with many parents and teachers wondering why this was not the case.
Dr Mary Bousted, joint general secretary of the National Education Union, said: “What is right for London is right for the rest of the country.
"It is time for the Government to protect its citizens, and in particular its children, by shutting all primary schools for two weeks in order for the situation to be properly assessed, schools made much safer and children and their families protected."
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