It is "vitally important" children go back to school, with the life chances of a generation at stake, Boris Johnson has said in a message to parents.
As the autumn term began in Northern Ireland, the prime minister said the risk of contracting coronavirus at schools across the UK was "very small".
He said missing any more school was "far more damaging" for children.
Meanwhile No 10 said it had "no plans" to follow Scotland in reviewing rules on wearing face coverings at school.
But the BBC understands the government is considering measures which could see secondary schools operating on a rota in parts of England where there are Covid-19 outbreaks.
Guidance 'silent' on masks
On face coverings, Scotland's First Minister Nicola Sturgeon said a consultation on their use in corridors and communal areas of secondary schools was in its "final stages".
It follows guidance from the World Health Organization that children over the age of 12 should wear masks.
Since Scottish schools reopened last month, there have been several confirmed cases among pupils and staff, including at Kingspark School in Dundee, where 23 people - most of them adult staff - have tested positive and which has shut for two weeks.
Heads in England - where face coverings are not recommended for schools - are calling for more clarity on whether staff or pupils can choose to wear face coverings.
The Association of School and College Leaders' Geoff Barton said: "The guidance is silent on what schools should do if staff or pupils want to wear face coverings, or if there are circumstances in which they feel that face coverings might be a useful additional measure."
But a Downing Street spokesman said no such review was planned for England's schools, adding: "We are conscious of the fact that [face masks] would obstruct communication between teachers and pupils."
And Education Secretary Gavin Williamson said the government was not suggesting secondary pupils or teachers should wear face coverings because there was a system of controls in place that meant it wasn't necessary.
But he said there were "elements of discretion" in guidance for schools provided by Public Health England.
Some pupils in Northern Ireland returned to school on Monday, while term starts in England and Wales in September.
The government's pondering of measures that could see England's secondary schools operating on a rota system if necessary is part of discussions under way on four different levels of schools operating.
They aim to keep primary schools operating as normal wherever possible, with localised restrictions on secondary schools where needed to bring the R number down.
Updated guidelines for schools for coping with local outbreaks are expected within weeks.
Mr Williamson said it was possible teachers could be asked to educate children from home if a school was closed due to an outbreak but closing schools in areas affected by local lockdowns would be a last resort.
The education secretary also said every school would have home testing kits for coronavirus by the time they reopened.
Mr Johnson thanked school staff for spending the summer "making classrooms Covid-secure".
Citing comments from England's chief medical officer, Prof Chris Whitty, the prime minister said "nothing will have a greater effect on the life chances of our children than returning to school".
In a video message, he added it was the "best way" to help children with any mental health problems resulting from or exacerbated by lockdown.
Prof Whitty had said children were more likely to be harmed by not returning to school next month than if they caught coronavirus. He said evidence showed they "much less commonly" needed hospital treatment or became severely ill with coronavirus than adults.
According to the Office for National Statistics' latest data on ages, there were 10 deaths recorded as "due to Covid-19" among those aged 19 and under in England and Wales between March and June - and 46,725 deaths among those aged 20 and over.
And of the more than one million children who attended pre-school and primary schools in England in June, 70 children and 128 staff caught the virus, according to a Public Health England study published on Sunday.
It said most of the 30 outbreaks detected in that time had likely been caused by staff members infecting other staff or students, with only two outbreaks thought to have involved students infecting other students.
And it suggested children who went to school in June were more likely to catch coronavirus at home than at school.
Dr Jenny Harries, England's deputy chief medical officer, told BBC Breakfast the study should "reassure" teachers that transmission from students to teachers was rare.
But she said the higher risk of staff-to-staff transmission meant teachers should remember to maintain social distancing and good hand hygiene while on coffee breaks, "because that does seem to be a risk factor".
Dr Matthew Snape, associate professor in paediatrics at Oxford University, said the risk to children from Covid-19 appeared to be low but the risk was that pupils could pass the virus to each other on the playground or in the classroom and then go home and "take that infection into their household".
The NEU, the UK's largest teaching union, said schools were being let down by the lack of a "plan B" as they prepared to reopen.
It said more staff, extra teaching space and greater clarity on what to do if there was a spike in cases were needed for schools to reopen safely.
Paul Jackson, head teacher of a primary school in east London, told the BBC it would have been useful to have clearer guidance from the government for school leaders and additional funding to help to pay for extra cleaning and other resources.
"Whether you are a very small school, with maybe just 70 pupils or whether you are a large school like us with 750 pupils, the guidance issued is exactly the same," he said.
Kay Mountfield, head teacher at Sir William Borlase's Grammar School in Marlow, Buckinghamshire, told BBC Radio 4's Today programme her school would reopen with safety measures, such as Perspex screens around teachers' desks, and had hired marquees to provide extra classroom space.
She urged the government to set up a dedicated helpline for school leaders to advise on keeping sites safe.
Parents 'have to behave'
Gemma Fraser says when eight-year-old daughter Poppy bounded out of bed on her first day back to primary school in Edinburgh, the children abided by the new rules - and it was the parents who had to be reminded about social distancing.
"The major change is they have to stagger the start times - so my daughter's group is the first in, at 8.40am, and the first to leave," Gemma says.
"The idea is that there aren't as many parents in at the same time. But it's actually been the parents who've been struggling with socially distancing the most - we've had several emails from the school reminding us to stand 2m apart. It feels like being back at school yourself."
Gemma says the playground has been segregated for dropping off and pick-up times so parents don't congregate. There are also separate entrance and exit points.
"We've missed seeing each other as well," she adds. "So it's only natural we want to catch up - but we have to behave ourselves."
Shadow education secretary Kate Green accused the government of being "asleep at the wheel" on the reopening of schools.
She said ministers had spent the past two weeks "totally pre-occupied with their own exams fiasco when they should've been out supporting schools and reassuring parents".
Meanwhile in Northern Ireland, many pupils in years seven, 12 and 14 were back at school on Monday for the first time since March. But at least two schools were not opening as planned because of people testing positive for coronavirus.
Education Minister Peter Weir said opening schools was probably the "top priority" for the executive.
But he said that there would be "undoubtedly bumps along the road" and staff and pupils will have to adapt to a new way of working.
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