More people connected to the school were expected to be diagnosed with the virus as further test results were confirmed, agency officials said.
In a statement on its website, the school, which has more than 400 pupils and 60 children in its nursery, said it had noticed a higher than usual number of pupil absences early last week and notified the Health Protection Agency.
It confirmed its first case of swine flu on Friday, but five more people tested positive for the virus over the bank holiday weekend and a further 44 were confirmed with swine flu on Tuesday.
A Health Protection Agency spokeswoman said all those confirmed to have the virus were responding well to treatment.
"There are still a number of laboratory results outstanding and the numbers of confirmed cases at the school are expected to rise," she said.
The school, which is currently closed for half term, said a "deep clean" of its premises would take place during the holiday period.
Earlier, it was announced a two-year-old boy from Oxford was among four cases confirmed on Tuesday morning.
The boy was a "close household contact" of a 29-year-old woman already diagnosed with the virus, Oxfordshire Primary Care Trust said.
The Health Protection Agency said case numbers at the school were not a surprise
The 37-year-old man from Glasgow who is critically ill was said to have underlying health problems. He was admitted to the city's Victoria Infirmary on Thursday.
Scottish Health Secretary Nicola Sturgeon said: "It is not yet known whether flu was the cause of his illness, or whether it was incidental to it."
A third swine flu case has also been confirmed in Ireland.
The Irish Department of Health said the patient was a woman who recently travelled from New York.
In the UK, a Department of Health spokesman said the current cases had so far been mild, and the strategy of containing the spread with anti-viral drugs appeared to have been effective.
"But we must not be complacent - it is right to prepare for the possibility of a global pandemic," he said.
"The UK's arrangements are continuing to ensure that we are well-placed to deal with this new infection."
About 13,000 people around the world have been diagnosed with the virus.
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