The latest cases included five Year 7 pupils at Alleyn's School, in Dulwich, south-east London, who were off sick on Friday.
A pupil who visited the US during the Easter holidays had already been diagnosed with the H1N1 virus.
The school has become the fourth school to be closed by the Health Protection Agency and will remain shut until next Monday.
It announced Tamiflu anti-viral medication would be supplied to all 1,200 pupils as well as staff and parents began collecting doses tonight.
Headmaster Dr Colin Diggory said: "We have been working very closely with the HPA as soon as we were made aware of the possible infection of one of our pupils.
"It is as a direct result of this precaution that the HPA were able so quickly to identify others who have become infected.
"We are told by the HPA that the affected pupils are responding well to the Tamiflu treatment and that they are recovering well.
"It was a difficult decision to make to close the school, particularly with public examinations in the pipeline. However, we are making contingency plans for those pupils due to take exams."
One parent, Cornelia Miller, 45, a psychotherapist said her year-seven daughter, Zoe, was displaying some symptoms and would now have to be swabbed for swine flu, as would the rest of the family.
She said her daughter did not know the children who had fallen ill, adding: "It is a friendly school, they all have parties and they mix a lot. My daughter has been ill since Wednesday but kids do get sniffles all the time.
"The school has been fantastic. It's a Bank Holiday Monday and all the staff are in. They've been brilliant."
But Year 12 students said they were concerned about effect of the closure on forthcoming exams.
Charlotte Bailey-Wood, 17, has French and Spanish oral exams in the next fortnight.
She said: "I'm in my last year and the last thing I want is to catch anything that will hold me back from doing my best.
"It's just really shocking because it's the last thing that you expect happening to your school."
Matthew Syrett, 17, said: "If exams are put off it gives us more time to revise at home, but we miss quite a lot of material that we could cover with the teachers in that time. A lot of the teachers haven't finished the syllabus yet."
In addition to the five Alleyn's students, two other children - London-based siblings who are close contacts of a previously confirmed case - were confirmed as having the virus today, the HPA said.
Two adults - who recently returned from Mexico - from London and the West Midlands were also diagnosed with swine flu today.
A Department of Health spokesman said seven of the cases confirmed today appeared to have been acquired from person-to-person contact.
"Nine new cases of swine flu have been confirmed in the UK - one in the West Midlands and eight in London.
"Seven of the nine cases appear to have been acquired through person-to-person spread. Two cases are in people who have recently returned from Mexico.
"There are now 27 confirmed cases in the UK - 23 in England and four in Scotland.
"The arrangements in place across the UK are continuing to ensure that we are well-placed to deal with this new infection."
A spokesman for the HPA said: "Those who are still unwell are receiving anti-viral treatment and are recovering at home.
"The Health Protection Agency is working to ensure that any close contacts of these cases are offered anti-virals as a precautionary measure."
A spokesman for NHS London said 13 cases of swine flu have now been confirmed in the capital.
"NHS London is working closely with the HPA and Southwark PCT to take all the necessary action to contain the outbreak at the Alleyn's School," he said.
The London adult confirmed with swine flu today is from the Hammersmith and Fulham borough and had recently returned from Mexico, he said.
The HPA said more than 300 suspected swine flu cases are currently being tested.
Alleyn's is the fourth UK school to be closed as a result of swine flu.
South Hampstead High School in north west London, Downend School in South Gloucestershire and Paignton Community and Sports College in Devon have already closed.
World Health Organisation (WHO) spokesman Dick Thompson today said the agency may raise its pandemic level from five to its highest alert, level six.
Spain's Health Ministry said 54 cases have now been confirmed in the hardest-hit nation in Europe.
Portugal confirmed its first case today, a 30-year-old woman who recently returned from a holiday in Mexico.
France confirmed two new cases in people who had been to Mexico, taking the total number to four.
Environment Secretary Hilary Benn today said Britain must remain vigilant although the flu was "relatively mild and responds well to treatment here in the UK".
"It's best to play safe in relation to this. We are still not absolutely sure what it is that we are dealing with," Mr Benn told GMTV.
Health Secretary Alan Johnson told the BBC he expects a second, more serious, wave of cases later this year.
The Department of Health's swine flu information line is on 0800 1513 513.
