Schools are drawing up plans to go part-time if the testing chaos continues, The Telegraph has learned.
Headteachers have said that unless the Government can get a grip on the testing system, they will need to instigate rota systems where pupils are taught on two weeks on, two weeks off basis.
Education leaders warned the Prime Minister that nearly every school in the country is struggling to access tests for students and staff.
Secondary schools should only move to a rota system if cases are rising in a local area and “all other measures have been exhausted”, according to official contingency planning advice published by The Department for Education.
But Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), said that teachers may be forced to put the rota plans in place sooner rather than later.
He said that the system is “unravelling”, with thousands pupils and teachers having to stay at home while they wait around for tests.
“I think we will start to see rota systems bought in because there are people waiting for tests and you simply can’t cover all the classes,” he told The Telegraph.
"Schools will worry about whether in fact the only way to ensure you have sufficient teachers is to move to a rota. I am not trying to scaremonger, but this does appear to be unravelling."
The reopening of schools has meant entire year groups or even whole schools have been sent home because children with symptoms are often unable to get a test to prove whether or not they have coronavirus.
If a pupil or staff member does test positive, headteachers have reported difficulties in accessing advice from public health officials about who should self-isolate and so are sending large numbers of pupils home as a precautionary measure.
Meanwhile Paul Whiteman, general secretary of the National Association of Headteachers, said that the strain on schools due to testing delays has become “intolerable”.
“We have examples coming in on individuals and groups of children being sat at home for extended periods of time waiting for a test,” he said.
Mr Whiteman warned that the system is not bought under control soon, schools will have to take action.
“You would be playing with ideas of different sized bubbles, you would be considering rota systems which are not completely desirable,” he said.
“The Government has been avoiding conversations about the ‘what ifs’ but very quickly the ‘what ifs’ are coming to pass.”
School leaders wrote to Boris Johnson on Wednesday to convey their "mounting concern" about delays in accessing test results and advice from public health officials, urging him to take personal control of the situation.
They said nearly 96 per cent of schools are experiencing difficulties and delays in accessing tests for students and staff, which is causing severe disruption to children's education.
The leaders of the country's two largest headteacher unions and the national school governor association said schools were left in an "impossible" position of "either leaving close contacts of the infected person in school while they wait for guidance, or making a public health call themselves and deciding on who to send home".
Their letter came as MPs told the Prime Minister that "everything will fall over" if schools don't have enough tests.
Boris Johnson told the liaison committee that it would be "wrong" for the whole class to be sent home if they have not tested positive.