Four families have been told they can apply for government compensation over side-effects of the Pandemrix swine flu vaccine.
Studies have shown the jab increased the risk of narcolepsy tenfold.
Families could be entitled to £120,000 through the Vaccine Damage Payments Scheme if they can prove "severe" disability.
If the bid fails they and other families could still pursue compensation through the courts.
Pandemrix was the most widely used flu vaccine in the UK during the 2009-10 pandemic. Almost six million doses were given, one million to young children.
However, evidence from across Europe has suggested a higher rate of narcolepsy in children after being given the jab.
Approximately one in 55,000 children vaccinated - about 20 in the UK - were thought to have developed narcolepsy.
The sleeping disorder causes people to fall asleep suddenly and unexpectedly. It can be hugely disruptive to daily life.
Compensation had previously been rejected on the ground that a link had not been proved. This has now been reassessed in light of the latest research.
A spokesperson for the Department for Work and Pensions, which runs the Vaccine Damage Payments Scheme, said: "DWP has looked at some vaccine damage payments cases again in light of new information regarding swine flu and narcolepsy provided by the Department for Health.
"We cannot comment on the specifics of individual cases but can confirm that once this new information was taken into account it was decided, on balance of probability, in some cases that causation was proved."
They will have to pass the department's "severe disablement" test.
'Evidence at the time'
The Department of Health said: "Pandemrix was developed specifically for use in a flu pandemic when the number of lives lost and serious cases could have been enormous.
"The decision to recommend that children got this vaccine during the flu pandemic was based on evidence available at the time, along with the advice from the European Medicines Agency, which approved its use.
"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."