A council leader has warned ministers schools could be "paralysed" if coronavirus testing is not increased.
Reading Borough Council leader Jason Brock said teachers and pupils were being forced to isolate for 14 days whenever there was any suspicion of a case due to inadequate testing capacity.
Cases have increased in the town over the past few weeks, he said.
The government said it was seeing a "significant demand" for tests.
In a joint letter Mr Brock, along with education lead councillor Ashley Pearce, told Education Secretary Gavin Williamson: "Whilst our infection rates in Reading remain below the level that would add us on to the government watchlist we have, like many other parts of the country, seen a steady increase in cases over the last few weeks.
"Without adequate testing capacity in place, teaching staff and pupils are being forced to isolate for 14 days whenever there is any suspicion of a case.
"This will continue to put enormous pressure on already exhausted staff at a time when they are dealing with many additional demands, including understandable parental anxiety."
The councillors are calling for adequate testing capacity, and prioritisation for teaching staff and pupils alongside key workers.
Hamilton School has already been forced to temporarily shut. It said a significant number of staff were displaying symptoms of the virus but they had no confirmed cases.
Prime Minister Boris Johnson is blaming a 'colossal spike' in demand for the ongoing problems with the testing system.
A government spokeswoman said testing capacity was at the highest it has ever been.
She said: "If a positive case is confirmed in a school, swift action is being taken to ask those who have been in close contact to self-isolate, and Public Health England's local health protection teams continue to support and advise schools in this situation.
"Children who are self-isolating will receive remote education. We will continue to work with schools to ensure all appropriate steps are taken to keep pupils and staff safe."