All children aged two to eight should receive a free nasal spray each winter, but last year only a third of two to four year-olds in the county were vaccinated.
Health officials say false rumours being circulated about the potential side-effects of the vaccine are discouraging parents from vaccinating their child – placing their health at risk.
Dr Neil Myers, from Rowe Avenue Surgery, in Peacehaven, said: “Children’s tactile nature and the fact they may not be aware of the importance of hygiene means they can quickly pass on the virus to others, even when they have no symptoms.
“It’s very unfortunate that myths spread online mean some parents are being deterred from having their children vaccinated.
“I would strongly urge parents to ignore the rumours and instead listen to expert medical advice and ensure their child is protected through this safe, painless nasal spray.”
Rumours circulating on social media have included exaggerated stories about potential side-effects, and the false claim that the flu vaccine can give people flu.
Flu – an acute viral infection of the nose, mouth, throat, bronchial tubes and lungs – can cause fever, chills, headaches, muscle and joint pain and fatigue.
Flu is not just a bad cold and often leads to children and adults needing several days in bed unwell.
Parents are urged to ensure their child has the nasal spray even if they had it last year, to protect against different strains of flu which change annually.
Cynthia Lyons, East Sussex acting director of public health, said: “Flu is an extremely unpleasant illness which can lead to young children being hospitalised and can even be fatal.
“The flu nasal spray is the best way we have of protecting children and the wider public against this unpleasant illness and has an excellent safety record.
“It is given to millions of children worldwide and the chances of suffering an adverse reaction are extremely low.”
Parents of two to four-year-olds can book a free vaccination through their GP while school age children up to year four can be vaccinated at school.
More information is available at www.nhs.uk/conditions/flu