The first official figures for school attendance in England for the autumn term show 88% of pupils went back.
This is a higher absence rate than the usual figure of about 5% but it is not broken down to show whether pupils were at home because of Covid outbreaks.
The figures show attendance last Thursday, based on responses from almost three quarters of state schools.
Since the reopening, school leaders have warned that delays in testing are leading to year groups being sent home.
In the run-up to the new term the government called on parents to send their children back to school, with the assurance that safety measures would be in place to protect them from the spread of Covid-19.
There had been speculation that some parents would keep their children at home - but the Department for Education figures show almost nine in 10 returned.
The department also estimates that 92% of all state schools in England were fully open - and that 99.9% were at least partially open.
However, there have been repeated local cases of schools having to send home year groups of pupils, either because of infections or because of problems with getting Covid tests for staff or pupils:
- On Tuesday, nearly 300 pupils at the Royal Wootton Bassett Academy in Wiltshire were sent home after a Covid case
- and at Bishop Fox's school in Taunton, Somerset there are 415 pupils self isolating in response to Covid infections
- on Monday, Steve Chalke, head of the Oasis academy trust, said about 1,200 pupils had been sent home from their schools, in a way which he said had become "rotation by default"
- while a survey by Teacher Tapp of more than 6,000 teachers suggested 3% of schools had sent home year groups or classes last week and 4% of teachers were self-isolating this week
The guidance for the safe reopening of schools in England had promised: "The government will ensure that it is as easy as possible to get a test through a wide range of routes that are locally accessible, fast and convenient."
But the National Association of Head Teachers, while welcoming the numbers returning to school, warned that problems getting tests was "causing chaos for schools right now and could jeopardise attendance remaining high".
The WorthLess? network of 5,000 head teachers warned that lack of access to tests could create staff shortages and force schools into partial closure.
Sean Maher, head of Richard Challoner School in New Malden, Surrey, said the Covid testing system had become a "complete and utter shambles".
He said students wanted to be back in school, but there had been 70 away on Monday, with many of these absences attributable to the difficulties in getting tests.
The Netmums online parents' network has written an open letter to the government complaining about the difficulties for parents who are struggling to get a Covid test.
"It's broken, not working and needs fixing. Our children have been back at school for a week or so, and already the testing system is at breaking point. And so are we," says the letter.
England's Education Secretary Gavin Williamson said: "The best place for children and young people to learn is in the classroom, and it's encouraging to see that last week more than seven million pupils were back with their classmates and teachers at schools around the country."