The latest figures put the number of people who have died from flu this winter at 27, including nine children.
According to the Health Protection Agency (HPA), 24 people were suffering from swine flu, while three had the flu type B strain. The figures represent the number of confirmed deaths from flu in the UK since October.
While almost half of those who had died were classed as "at risk" - such as suffering from asthma, heart disease or diabetes - only one person who died (and whose vaccination status was known) had received the vaccine this year.
The HPA would not confirm whether anyone who had died had been pregnant, because of concerns over identification.
A spokeswoman for the HPA said the flu jab was only 70% to 80% effective, meaning somebody could still potentially die from flu if they were vaccinated but had an underlying serious illness.
"It is not a vaccine failure; it means the person's illness is so serious that they are very weak."
Latest figures show rates of flu infection have more than doubled in the last week.
Cases of flu have risen to 87.1 per 100,000 people, from 32.8 in the previous week, according to England and Wales data from the Royal College of GPs.
Rates of flu are highest in youngsters aged five to 14, followed by those under four, then people aged 15 to 44.
Professor Dame Sally Davies, interim chief medical officer for England, said rates of flu were within the expected range for the time of year.
"Clearly, any death is sad for the family and the patient and we don't like it," she told the BBC.
"But 27 deaths at this stage of seasonal flu is not a large number."
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