Health experts have called for parents to ensure their children have the flu vaccine if they fall into at-risk groups.
The Royal College of Paediatrics and Child Health (RCPCH) made the call as the virus tightens its grip on the UK.
The body expressed concern over the rising number of people contracting flu and how children were being affected.
A total of 39 people in the UK have died of flu since October, according to figures published on New Year's Eve.
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.
Flu has been striking the under-65s, with relatively high rates in youngsters under 15.
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."