Heads say the financial implications of covering staff absence during the swine flu outbreak could put strain on school budgets which are already due to decline.
In Wales, heads have warned that swine flu could force cash-strapped schools to close within weeks of the new term because they will be unable to afford cover for absent teachers.
They told The TES they would not have the financial resources to cope if even a small number of their staff were struck down.
Neil Foden, head of Ysgol Friars in Bangor, said many schools would be forced to spend cash set aside for unforeseen circumstances to plug holes in their budgets.
"Because the Government has kept schools and councils so starved of cash we have no financial contingency," he said. "If a pandemic does occur and a lot of teachers are off sick I don't know how we would cope. Schools just don't have the financial flexibility."
Mr Foden said his 1,250-pupil school would be forced to close if 10 of his 80 teachers became ill at the same time.
David Fann, head of Sherwood primary, Preston, said: "I normally have pound;14,000 in my budget for supply, which includes an insurance premium of pound;7,000. As far as I'm aware no school has budgeted for a pandemic like this.
"If there are many more absences in September, there will be problems with the budget. If we end up with a loss then we will have to look at reducing staffing."
John Lambert, head of Rawmarsh Community School, Rotherham, said: "The real problem comes when teachers have to stay off to look after their families. That is an unknown."
Meanwhile, in England unions have called for teachers to be considered as a priority for the swine flu vaccine.
The NUT has written to Schools Secretary Ed Balls saying: "Offering protection to staff and pupils will help ensure schools can stay open and avoid disruption to pupils' education."