Redbridge Council has become the latest local authority in London to suggest schools move to online teaching amid a rise in coronavirus cases.
It comes after Greenwich and Islington Council backed down from a similar decision when the government threatened legal action.
Schools minister Nick Gibb has also written to Waltham Forest Council after it asked schools to close.
He said he was “deeply disappointed” by the councils’ choices.
BBC Newsnight’s Lewis Goodall said 7,000 pupils in Redbridge were self-isolating as of Monday.
Redbridge Council said it believed schools should now consider whether they could remain open for all pupils or move to remote learning if absences were high enough.
A total of 32 schools in the borough will close on Wednesday and move online, the council said.
Another 25 will stay open – 12 of which are taking an extra day to decide if they will close their classrooms.
In a letter seen by the BBC, council leader Jas Athwal said: “Unfortunately, cases of Covid-19 continue to rise across the borough, and as a result, some of our schools are struggling to continue to provide the high-quality in-person teaching our children deserve.
“It is not the role of the council to close schools, but today we want to be absolutely clear – we will support our local schools if they choose to move to online learning.”
London, most of Essex and parts of Hertfordshire will move into England’s highest tier of Covid restrictions on Wednesday due to a rise in infections.
Schools in England were told they could close a day early for Christmas last week to give staff a “proper break”.
In Basildon, where the country’s third-highest Covid rate was recorded, schools were also allowed to close early, while London’s mayor Sadiq Khan has called on secondary schools and colleges in the capital to follow suit.
Earlier the leader of Greenwich Council said he had “no choice” but to ask schools to remain open after threats of legal action from the government.
The authority wrote to head teachers asking for classes to move online from Tuesday amid rising Covid-19 cases, but Education Secretary Gavin Williamson ordered the council to keep all schools open until the end of term.
On Tuesday morning two other local authorities – Islington and Waltham Forest Councils – advised schools to move to online learning for the last few days of term amid rising Covid-19 rates in other parts of the capital.
But, by the evening Islington Council’s leader Richard Watts had backtracked on this decision.
He said: “After discussion today with the Department for Education, we have now advised our schools to open as usual to pupils on Wednesday, and advised our schools that they are able to arrange an INSET day on Thursday. Friday was to be an INSET day already.”
Schools Minister Mr Gibb had written to Islington and Waltham Forest asking them to reconsider their decisions to close schools and stating legal action would be considered if they did not.
However, Waltham Forest Council’s leader Clare Coghill said she had “received no correspondence” from Mr Gibb.
The decision to remain open or closed was left to individual schools in Waltham Forest, she added.
“We are confident that schools in Waltham Forest have made their decisions on the basis of their own individual risk assessment and with pupil safety at their heart.
“It is disappointing that, during a year when teachers, pupils and parents have made extraordinary efforts to ensure education continues through a once-in-a-lifetime crisis, the Minister has chosen to write to our schools threatening them with potential legal action.
“We will continue to do all we can to support schools to make the decisions that will safeguard the health and safety of pupils, teachers and their families and ensure children continue to be educated.”