Birmingham girl dies of swine flu
Sir Liam said: "We still think we are heading for the largest surge of cases in the autumn and winter."
Dr Vivienne Nathanson, head of science and ethics at the British Medical Association, said: "The fact is that any kind of flu can kill people of any age.
"Flu can kill even completely healthy people if they get pneumonia but, if they have got other health problems, they are more likely to get complications.
"Most of the people with swine flu have been saved. There will be occasional tragedies and, of course, every death is a tragedy. But it's important that people do not panic. It is expected that there will be deaths."
She said the Health Protection Agency (HPA) is watching closely to work out the rate and type of complications from swine flu.
"As we get more and more data, we can start to assess exactly the kind of complications and we may start to be able to identify groups at higher risk.
"This will help us in the future when we have a vaccine - to be able to vaccinate the people at highest risk."
Dr Nathanson said experts were being "very, very fastidious" at chasing down cases and recording data that was being used to inform the response to the pandemic.
Health Secretary Andy Burnham said: "I would like to express my condolences to the patient's family at this very difficult time. This is a tragedy for those concerned and they have my heartfelt sympathy.
"Tragic as today's death is, I would like to emphasise that, across England, the majority of swine flu cases have not been severe. I would reiterate that the risk to the general public remains low and we can all play our part in slowing the spread of the virus by following simple hygiene procedures - like washing your hands and using tissues when coughing or sneezing.
"We continue to monitor the situation very closely, making sure arrangements are in place so that the UK remains well-placed to deal with this pandemic."
A 73-year-old man from the Inverclyde area died at the Royal Alexandra Hospital in Paisley, Scotland, on Saturday night.
The unnamed man, who, like the Birmingham girl, had serious underlying health conditions, had been treated in the hospital's Intensive Care Unit for the past 15 days.
The first UK fatality, Jacqui Flemming, 38, who had just given birth prematurely, died two weeks ago at the same hospital. She also had other health problems.
Elsewhere, six revellers were sent home from the Glastonbury festival over the weekend with suspected swine flu and three or four ball boys and girls suffering from a "flu-like illness" were asked to stay away from the Wimbledon tennis tournament.