Telling schools to switch to remote learning was "the brave decision the government was not willing to face", Brighton & Hove City Council has said.
It has advised primary schools to teach most pupils online until 18 January to keep children, school staff and the wider community "as safe as possible".
In Kent, the county council has called for all its primary schools to "have breathing space" before reopening.
But Surrey County Council has told its primary schools to open as normal.
A Department for Education spokesman said: "Children's education has consistently been a national priority, which is why we want classrooms to reopen wherever possible in the new term."
Head teachers across the country have warned of a "confusing picture" with some schools staying shut, after union safety warnings.
In Brighton, leader of the Green-controlled council Phélim Mac Cafferty has written to the Education Secretary, Gavin Williamson, to ask him to include the city's primary schools in the list of schools that have moved to remote learning.
The city council's deputy leader and chair for children, young people and skills, Hannah Clare, said: "We feel we have made the brave decision that the government wasn't willing to face."
'Rapidly changing situation'
In Kent, the county council has asked Mr Williamson for a delay in reopening primary schools in four parts of the county.
In other areas they are already closed to most pupils.
Surrey County Council has requested primary schools in the county open as normal "in line with government guidance".
But it said it would continue to monitor "the rapidly changing national situation closely".
East Sussex County Council said "several" primary schools had been able to open as planned and some had decided they were not able to open.
"We understand this is a fast-moving and challenging situation," a council spokeswoman said.
West Sussex County Council tweeted: "We are aware that some West Sussex primary schools have not been able to open for face to face teaching for all pupils today as scheduled and we are working with them on opening as soon as they can with sufficient staff to ensure that pupils can be managed safely."
School staff across the country have taken union advice to teach remotely on safety grounds.
National Education Union representative Phil Clarke said it was about "protecting communities, protecting hospitals, as well as schools".