Parents were urged today to get their children vaccinated against flu if they fall into at-risk groups.
The Royal College of Paediatrics and Child Health (RCPCH) said it was "concerned" about the rising number of flu cases, and how it is affecting younger children.
Flu has been striking the under-65s, with relatively high rates in youngsters under 15.
The most recent figures on numbers of deaths, published on New Year's Eve, showed 39 people in the UK have died with flu since the start of the outbreak in October.
Of these, 36 had swine flu and another three had flu type B. Overall, 38 of the 39 victims were aged under 65, with four aged under five.
The Government has so far resisted calls for a national vaccination programme of young children, as was carried out last year for swine flu.
The RCPCH said it was "concerned" at the rising number of flu cases.
"We would therefore encourage all children who are in an at-risk group, such as reduced immunity, breathing difficulties and diabetes - who have not yet been vaccinated, to take up the offer of the vaccination.
"Paediatricians are working closely alongside other medical colleagues, both in community and hospital settings to provide services to children and their families.
"The Department of Health has provided good advice about how to avoid catching and spreading the virus."
Children fall into at-risk groups if they have a chronic respiratory disease (including asthma), chronic neurological, heart, kidney or liver disease; diabetes or a weak immune system.
The call comes as experts warned of a rise in new cases as people return to work and school following the holidays.
Professor John Oxford, an expert in virology at St Bartholomew's and the Royal London Hospital, said the return of children to school had in the past prompted a rise in the number of flu cases.
"You tend to get a surge," he said. "I would anticipate a surge, but how long that will last is difficult to say.
"This virus is not going to go away next week. Even if it's already peaked, it's still going to be around for the next couple of weeks and it's still worthwhile being vaccinated at this stage."
Although closing schools in response to flu pandemics had not proved effective, Prof Oxford said parents were far from "powerless" and could aid the fight against the virus by ensuring good hand hygiene and keeping children away from others with the illness where possible.
Dr Douglas Fleming, director of the Royal College of General Practitioners' research and surveillance centre, also voiced concern that the current flu outbreak may not have peaked despite the fact that a large number of children had already had the virus.
He said: "I personally don't feel that we have quite reached the peak."
The number of people in critical care (intensive care and high dependency beds) on Thursday stood at 738 across England, including 42 youngsters under five.
The Joint Committee on Vaccination and Immunisation (JCVI) has said it does not recommend the Government implement vaccination for children under 15 unless they fall into at-risk groups.
It said last week that "although there is a high incidence of influenza-like illness currently in these age groups, a significant proportion of this is due to other viruses such respiratory syncytial virus (RSV).
"In addition, only a very small proportion of those with severe disease are in these age groups."
The National Pharmacy Association (NPA) said members of the public have been asking pharmacists about the flu vaccination, including for children.
It "encourages the public to protect themselves against flu by observing good hand hygiene and considering the latest seasonal vaccine which protects against seasonal flu strains, including the H1N1 swine flu virus".
But the NPA said "children are generally not eligible for vaccinations administered in pharmacies".
"Whilst pharmacies are naturally reluctant to turn people away, they can only offer the service where the pharmacist has received appropriate training.
"Pharmacists would need to undergo additional, specialised training in order to vaccinate children."Reuse content