"There are three further confirmed cases, one a 12-year-old girl from Torbay, two other adults, one from Birmingham and one from London," Prime Minister Gordon Brown told Parliament.
The Torbay school attended by the sick girl has been closed, with all students being vaccinated with Tamiflu as part of preventive measures.
Brown also pledged efforts to increase the number of vaccines to 50 million from the current 35 million in the country.
Britain's first two swine flu cases were confirmed on Monday in two newlyweds from Scotland who had just returned from a honeymoon in Mexico.
Mexico's health minister, Jose Angel Cordova, said earlier on Wednesday that only seven deaths in the Central American country could be said without doubt to have been caused by swine flu. His comments came amid reports saying that up to 159 people in the country had died of "suspected" swine flu.
The World Health Organization has raised the level of swine flu pandemic alert from phase 3 to 4, implying a significant risk increase, two steps short of a full pandemic.
