Most of those who died had swine flu. The majority were aged between 15 and 64, but nine children under 14 died.
An HPA spokesman said the number of people seeing their GP for flu-like illness was beginning to plateau.
Of the 81 deaths where data is available, 63 people were in risk groups for flu.
And of the 47 for whom vaccine status is known, 40 had not had this season's flu jab.
Since October, 95 deaths have been linked to swine flu and 12 to the influenza B virus, with the rest unclassified.
Cases not soaringProfessor Sally Davies, Interim Chief Medical Officer for
The HPA reports only verified deaths, so while it appears as though the number dying from flu had doubled in the past week, the figure seems larger because of the time it takes to confirm the cause of death.
Professor Davies was reluctant to say the outbreak had peaked, but added: "I hope we'll have good news, maybe not next week because of schools going back, but the week after."
And she appealed to parents of children with underlying health conditions to have their children vaccinated.
"Their parents must take them to have the vaccination as soon as they can."
Last week it was announced that jabs left over from the swine flu pandemic would be made available after some GP's practices reported a shortage of this year's vaccine.
More than 200,000 doses have been ordered.
Professor David Salisbury, director of immunisations at the Department of Health, said: "No one should be turned away because of a shortage of vaccine. There is no reason to turn away at-risk patients."
Bacterial infectionsThe HPA said though that the figures only represented a proportion of those who had died from flu, or from complications such as pneumonia.
However, deaths are far fewer than the 500 seen during the swine flu pandemic in 2009.
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Our latest flu report suggests levels of people seeing their doctor for flu-like illness is beginning to plateau ”
End Quote Professor John Watson, HPA Head of respiratory diseasesThe number of people in critical care beds in
Professor John Watson, head of respiratory diseases at the HPA, said: "Our latest flu report suggests levels of people seeing their doctor for flu-like illness is beginning to plateau but this may be skewed by the recent holiday period.
"Flu is still circulating in the community and the message remains that those people in an at-risk group should have their seasonal flu vaccine as soon as possible as this is the best way to protect themselves from flu this winter."
At-risk groups who are advised to have the jab include pregnant women, the elderly and those with other underlying conditions such as heart problems, diabetes, lung, liver or renal diseases and those who have weakened immune systems.
The HPA added that it had seen a "modest" increase in bacterial infections such as pneumococcal and meningococcal disease, which might be linked to flu, and that it was advising doctors to remain vigilant for them.
Professor Watson added: "The severity of these conditions means that prompt identification and treatment are essential."
Professor John Oxford, a virologist at Barts and the Royal London, suggested the outbreak might be "past the worst".
But he told the BBC it was important for government and experts like himself to learn lessons.
"It was much bigger than we thought. We should think much more seriously about vaccinating the under-fours."