The parents claim that the Pandemrix vaccine led to their kids developing the disorder, which causes excessive daytime sleepiness.
Now research by the Health Protection Agency, published in the British Medical Journal, suggests that for every 55,000 doses of the drug delivered, around one child developed narcolopsy.
Health experts reassured parents that the many children who received the jab are well and are expected to 'remain fine' because symptoms appear to develop a few months after the vaccine is given.
The research examined 75 children aged between four and 18 who were diagnosed with narcolepsy from January 2008 and who attended sleep centres throughout England.
Researchers from the Health Protection Agency and Papworth and Addenbrooke's hospitals in Cambridge found that 11 of these had received the vaccine before their symptoms began.
The authors associated the vaccination with a 14-fold increased risk of narcolepsy.
Professor Liz Miller, a consultant epidemiologist with the agency and lead author of the report, said: "These findings suggest there is an increased risk in children of narcolepsy after Pandemrix vaccination and this is consistent with findings from studies in other European countries.
"Long-term follow up of people exposed to Pandemrix is needed before we can fully establish the extent of the association."
The agency's findings are likely to help parents seeking damages, who claim the jab gave their children narcolepsy.
Caroline Hadfield, 42, from Frome in Somerset, is suing the Government because her son Josh, seven, developed the condition within weeks of being vaccinated in 2010.
She said he sometimes slept for 19 hours a day before being diagnosed and receiving medication to control the condition.
At the height of the swine-flu pandemic, between October 2009 and March 2010, more than 850,000 children in England aged six months to 16 years were given the vaccine.
The jab was also administered to 170,000 adults and children when supplies of the seasonal flu vaccine diminished from Oct 2010 to Feb 2011.
A Department of Health spokesman said: "We keep all emerging evidence under review and that's why use of Pandemrix in those less than 20 years old was stopped in the UK in 2011."
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