Most children are offered the vaccine in a nasal spray rather than an injection.

NHS England's weekly flu and Covid surveillance report said there was increased flu activity "particularly among children".

Duncan Burton, chief nursing officer for England, said it was concerning that the flu had hit early this year and the increase among children was "worrying".

"Flu can spread like wildfire across schools and can make children really unwell," he said.

"The virus changes each year, so vaccination remains the best way to shield your child from getting seriously ill."

He urged parents to make sure they had opted their child in for an in-school vaccine or find their nearest clinic.

Pop-up clinics were being held in places like bowling alleys and fire stations, Mr Burton told BBC Radio 4's Today programme, adding that the vaccine was "quick, easy and safe".

Dr Fari Ahmad told BBC Breakfast that while she was seeing cases, "I don't think we've quite hit the peak yet".

"With flu, this is a war we have every year. Flu is unpredictable, it still kills people and every year we try to get enough people vaccinated so that when the big surge comes we are not decimated," she said.

Dr Ahmad said that getting enough school-age children vaccinated meant that it made that surge better, "because they are spreaders".

"It will be great for the kids individually but it will also be better for all of us," she said.

NHS England said more than 10 million vaccines have already been delivered in the latest campaign, including to almost 1.5 million school-aged children and more than 300,000 eligible two and three year olds.

Free vaccines are available to those older than 65, with certain long-term health conditions, are pregnant, live in a care home, the main carer for an older or disabled person or live with someone who has a weakened immune system.

Parents urged to vaccinate children as flu cases rise