Public Health England and NHS England in Yorkshire and the Humber issued the warning after statistics showed that just under 9,800 two-year-olds and 10,000 three-year-olds have been vaccinated so far, meaning around 72,000 are still unprotected.
As the weather gets colder and flu numbers increase, this could prove dangerous for younger children.
Sally Eapen Simon, screening and immunisation lead, said: “It is very important for children to be vaccinated with the free flu vaccine so they can stay well. Flu can be a very serious illness. Healthy children under the age of five are more likely to be admitted to hospital with flu than any other age group.
“Young children are also ‘super-spreaders’ of flu, so we know that if we vaccinate children against flu this also protects their grandparents and other vulnerable people around them who are more at risk of developing serious complications.
“Our message is to get your two and three year old children vaccinated against flu at the GP as soon as possible before flu starts to spread locally, so they don’t get poorly.’
Last year’s flu vaccination programme reduced the risk of flu in children by 65 per cent. For healthy children aged two to eight, the flu vaccine is given in the form of a nasal spray.
Mum-of four-Sarah Robertson said: “It was really easy as it just involved a little squirt up each nostril.
“If you are unsure at all, I found lots of useful information on www.nhs.uk.”