Chloe Buckley's school flew a flag at half mast in tribute to her
The health secretary has urged parents to keep swine flu in perspective following the death of a six-year-old girl who had contracted the illness.
Andy Burnham said "lots of children" had made a full recovery after suffering from the virus.
Tests continue to see if schoolgirl Chloe Buckley and GP Dr Michael Day had underlying health problems which may have contributed to their deaths.
There have now been 17 swine flu-related deaths in the UK.
Mr Burnham told GMTV: "There have been lots of children already having the condition but making a very quick and full recovery. We do have to keep it in perspective."
Chloe, who was from west London, died after contracting swine flu on Thursday.
A post-mortem examination is now due to be carried out to see if she had any pre-existing medical conditions.
She was a pupil at St Catherine's School in West Drayton, and on Monday night, teachers and council officials held a meeting to try to reassure other parents worried about their children's health.
Chris Spencer, director of education and children's services at Hillingdon Borough Council, said the school would close early for the summer break.
"This is a little girl who, until a few days ago, in all our minds was a child that was perfectly healthy so everybody here is in a deep state of shock."
Dr Day died on Saturday in Luton and Dunstable Hospital.
Tests confirmed he was suffering from swine flu, but as yet his exact cause of death is unknown.
Colleagues and patients at Priory Gardens health centre in Dunstable who have been in recent contact with him are now being assessed for symptoms of the virus.
A patient in Essex who died earlier this month was the first person in the UK without underlying health problems to die of swine flu.
Health officials have also urged the public not to panic despite the latest deaths.
Prof Steve Field, chairman of the Royal College of GPs, said his members had been "working with the government on robust flu pandemic plans for a number of years".
"We are confident that the systems we have in place will cope well with the current pandemic," he said.
Dr Laurence Buckman, chairman of the British Medical Association's GPs Committee, added: "We must remember that every year there are deaths from complications of seasonal flu - this is unfortunately inevitable with any strain of influenza."
Dr Chris Smith, a virologist at Cambridge University, said worldwide and UK data suggested the swine flu death rate was 0.5 or 0.4%.
"In other words about one person in every 200 who contracts this virus may die. And that's unfortunately inevitable. We don't know why this happens."
Scientists will now try to determine why the virus is fatal for some people, he added.
The government has ordered enough vaccines to cover the entire population, with the first doses arriving next month.
Dr Michael Day worked as a GP in Dunstable, Bedfordshire
But in the meantime, research by the University of Wisconsin and published in the journal Nature, suggests that the swine flu virus attacks the respiratory system in a more sustained way than the standard seasonal flu virus.
Liberal Democrat health spokesman Norman Lamb said dealing with the outbreak was a "mammoth task".
"The government needs to ensure that all frontline NHS staff are given access to flu vaccines as a matter of urgency," he said.
"It is extremely worrying that GPs are still raising concern over the lack of clarity over who should now be receiving anti-viral treatment."
But Mr Burnham said the government was well-prepared.
"We have been working closely with the Royal Colleges and staff bodies to protect and prepare frontline health workers, who are at the heart of our response to this outbreak, whilst providing the best health care possible to patients," he said.
The UK's chief medical adviser, Sir Liam Donaldson, said there is a reason why treatment appears inconsistent.
"There is an uneven pattern around the country in the spread of the disease. For example, in the south-east the levels are something like 10-times the level in the north of England.
"This is what you see in the early stages of a new virus coming out. It spreads unevenly around the country and you need to address it in different ways at different stages."