A 12-year-old girl is one of three more people confirmed with swine flu, Prime Minister Gordon Brown said today.
The girl, from Torbay in Devon, a 41-year-old woman from Redditch and a 22-year-old man from south London, were confirmed with the flu, he told the Commons.
The first two British cases were confirmed on Monday in Scotland.
All three new cases recently travelled to Mexico, the Prime Minister said. They displayed mild symptoms and were responding well to treatment.
The girl's school, Paignton Community College, has been closed for seven days and all other pupils offered anti-viral treatment.
The Health Secretary Alan Johnson said the 12-year-old was on the same flight from Mexico as the Askhams, the Scottish couple who have also been diagnosed with swine flu.
He added that all cases of swine flu so far are directly linked to Mexico and said the UK was taking steps to increase stockpiles of anti-virals to provide for 50 million people. Current stocks would cover 33 million - about half of the UK's population.
Mr Brown said the UK is taking "the preparations that are necessary and the precautions to prevent the incidence of this disease in this country".
Measures include enhanced airport checks, expanding anti-viral stocks from 35 million to 50 million, ordering extra face masks and printing an information leaflet for every family.
The extra masks will be used by health professionals such as nurses and doctors working with infected patients in the event of a pandemic.
The Department of Health has said the masks are not intended for members of the public, for whom they are thought to be of little use.
The information leaflets on the virus will be delivered across the UK in the coming days and will contain information about the flu outbreak and preventative messages.
The first two confirmed patients, Iain and Dawn Askham, of Polmont, near Falkirk, had been on honeymoon in Mexico and were being treated in isolation at Monklands Hospital in Airdrie, Lanarkshire, today.
Their parents said the newlywed couple were "shocked" at the positive test results.
Other countries with confirmed cases of swine flu are Mexico, the US, Canada, New Zealand, Germany, Austria, Spain and Israel.
In the US, government officials said swine flu killed a 23-month-old child, the first death reported outside Mexico.
The toddler died in Texas, Dr Richard Besser, acting director of the Centres for Disease Control and Prevention, said in an interview with CNN.
Staff at Paignton Community and Sports College referred all inquiries today to the local health authority, Torbay Care Trust.
A spokesman at Torbay Care Trust could not confirm which of the school's two sites had been closed but said a statement would be issued with further details.
Health Secretary Alan Johnson, who briefed the Premier on the new confirmed cases this morning, will make a statement to MPs this evening.