The new cases brought the number of confirmed victims in the UK to 18, with 14 in England and four in Scotland.
Another 716 possible cases of swine flu are under investigation.
One of the cases announced today was a 14-year-old girl from Barnet, north London, who caught the virus from somebody who had travelled to Mexico.
Her independent girls' school, South Hampstead High School, posted a letter to parents on its website saying the year nine student was "at home and well".
Antivirals have been offered to her year group, special arrangements are being made for upcoming exams, and the school will be closed until at least Thursday.
It is the third UK school to close since the virus began spreading, joining Downend School in South Gloucestershire and Paignton Community and Sports College in Devon.
The 14-year-old is also the third case in the UK of someone contracting the virus without first travelling to Mexico or the US.
The other English case announced today, an 11-year-old from Wandsworth, south west London, had travelled to the US.
An NHS London spokesman said: "Both cases are being treated at home with antiviral drugs and are responding to treatment.
"The Health Protection Agency is carrying out further tests on people who have had close contacts with these patients."
The HPA said the 11-year-old's school did not need to close "as the patient did not attend school while symptomatic".
The number of cases in London has now reached five. Other cases have been confirmed in Newcastle, Merseyside, Devon, Worcestershire, Gloucestershire, Oxfordshire and Central Scotland.
The third victim announced today was a man from Ayrshire, the fourth in the district to contract the disease.
Scottish health secretary Nicola Sturgeon said he had no connection to the three cases which have previously been confirmed in the area and that he had flown back from Houston, Texas, in the US on Monday.
Earlier today, Health secretary Alan Johnson said there will be more cases in the UK and warned of a second wave of infection during the autumn.
"Our evidence from all previous pandemics is that you get two phases. You get a first wave that is often very mild and then you get a much more serious wave that comes along in the autumn and the winter," he told BBC1's The Andrew Marr Show.
"So we have to not just deal with this outbreak now, but prepare, perhaps, for a second phase further down the line."
Although the World Health Organisation has declared a phase 5 alert level - one step short of declaring a pandemic - Mr Johnson said that the measures taken in the UK had proved effective in limiting the spread of the disease.
"Pandemic just describes the geographic spread, it doesn't describe the severity. So far ... I think it is contained."
An HPA spokesman said: "At this stage, with only a small number of cases of human to human transmission in the UK, this does not yet represent sustained human to human transmission.
"The cases of human to human transmission in the UK all had contact with individuals with illness and travel history to an affected area. The risk to the general public remains very low.
"Outside of Mexico, the majority of cases have been mild and cases have responded positively to anti viral treatment."
World health officials appear to have begun playing down the virulence of the flu strain.
Dr Michael Ryan, WHO Director of Global Alert and Response, said there was "no evidence of sustained community spread outside of North America".
He also praised European nations' handling of cases and said events did not seem out of control.
There have been at least 872 confirmed cases worldwide.
The death toll in Mexico stands at 19 and a 21-month old Mexican boy died after travelling to the US.
But the Mexican health minister today said the virus was in its "declining phase".
Jose Angel Cordova said the virus appeared to have peaked between April 23 and 28.
The virus has been confirmed in 19 countries worldwide - Mexico, the US, Canada, Spain, the UK, Germany, New Zealand, Italy, France, Israel, South Korea, Colombia, Costa Rica, Ireland, Switzerland, Austria, Hong Kong, Denmark and Holland.
Britain has the second-highest number of swine flu cases in Europe, after 40 confirmed cases in Spain.
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