The antidote, used during the swine flu pandemic that began in 2009, is associated with a 14-fold increase in a child's risk of the chronic disorder, which causes excessive sleepiness.
More than one million Pandemrix vaccines were distributed in Scotland during the swine flu pandemic and it was given to six million people in Britain.
Of those, more than 80,000 children aged six months to 16 years north of the Border were given the vaccine as well as 850,000 English children.
It was also given to 200,000 more in the UK when supplies of the seasonal flu vaccine diminished, from October 2010 to February 2011.
Concerns about the link resulted in a review of Pandemrix by the European Medicines Agency in August 2010, but the Scottish Government decided it would not be withdrawn as there were no linked cases of narcolepsy reported.
The research, published in the British Medical Journal, revealed that, for every 55,000 doses of the GlaxoSmithKline drug delivered, around one child developed the condition.
In total, 75 child narcolepsy sufferers who attended sleep centres across England were examined from January 2008. Researchers from the Health Protection Agency and Papworth and Addenbrooke's hospitals in Cambridge found 11 of them had received the vaccine before their symptoms began.
After adjusting for clinical conditions, the authors associated the vaccination with a 14-fold increase risk of narcolepsy. But health experts cautioned that many children who received the jab are well and are expected to remain fine as symptoms appear to develop a few months after the vaccine is given. The injection has not been in use for almost two years.
Narcolepsy, which is thought to affect 20,000 people in the UK, has a genetic component but has to be triggered by other factors for the condition to appear. It commonly includes bouts of daytime sleepiness, but can also bring nightmares, hallucinations, and cataplexies when strong emotions trigger a sudden loss of muscle strength. It has no known cure, but can be treated.
A Scottish Government spokesman said: "The results of the HPA study on narcolepsy are consistent with earlier evidence from some other EU countries. The Medicines and Healthcare Products Regulatory Agency confirmed the risk of developing narcolepsy following Pandemrix vaccine was very low. In Scotland, Pandemrix is no longer used.
"Current seasonal flu vaccines have not been linked to narcolepsy, and this issue has no implications for the safety of the seasonal flu vaccine programme or any other vaccines in current use."
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