Schools are operating on a "chaotic rota system by default", with two-thirds of secondaries sending pupils home because of Covid, heads have warned.
Widespread disruption is happening in an "ad hoc manner" because of the "unpredictability of outbreaks", making it "very difficult" for schools to plan and deliver lessons, according to the Association of School and College Leaders (ASCL).
The warning follows new government figures that show the proportion of schools with one or more pupils off self-isolating because of a coronavirus case has almost doubled in the space of a week.
Exclusive: One in three schools have Covid cases
Geoff Barton, ASCL general secretary, said: "These figures show a huge increase in the number of secondary schools having to send home pupils to self-isolate.
"It is clear that the improvement we saw following the half-term holiday was temporary and that the situation has worsened again very quickly.
"Disruption is widespread and is happening in an ad hoc manner because of the unpredictability of outbreaks.
"This makes it very difficult for schools to be able to plan and deliver lessons and catch-up support. This is exacerbated if there are also members of staff having to self-isolate.
"We understand the government’s desire to keep all pupils in school full-time. But when nearly two-thirds of secondaries are sending home pupils we have a chaotic rota system by default."
He added: "Schools need to be given more latitude to move to a planned rota system if they feel that this would be less disruptive, more manageable, and in the best interests of their pupils.
"It would give them the ability to deliver direct and remote learning around smaller groups rotating between school and home in a planned manner.
"The government has to recognise reality. The current situation is unsustainable."
Commenting on today's attendance figures, a spokesperson for the Department for Education said: "Over 99 per cent of schools have been open every week since term began and millions of pupils are continuing to benefit from being in school.
"The chief medical officer remains of the view that schools should remain open, and has highlighted the damage caused by not being in education to children's learning, development and mental health."