Scientists from the Health Protection Agency (HPA) found evidence of a link between GlaxoSmithKline's Pandemrix jab and narcolepsy cases in children earlier this year.
The vaccine was given to around 6m people in the UK in 2009-11. The HPA estimated that the vaccine could have caused narcolepsy in around one in every 55,000 cases in a study of four to 18-year-olds.
Law firm Hodge Jones & Allen said that compensation could be up to or possibly exceeding £1m for each case.
The firm said that GlaxoSmithKline have now invoked a Government indemnity agreed with the Department of Health in 2007, requiring compensation claims to be paid by the Government.
GlaxoSmithKline said that governments had agreed to share costs during vaccination programmes against the H1N1 pandemic flu which were "unprecedented in their scale and speed"
"Throughout development of our H1N1 flu vaccines there was no data suggesting a potential for an increased risk of narcolepsy among those vaccinated. We take the safety of patients who entrust their health in our medicines very seriously," a spokesperson for the company said.
Hodge Jones & Allen said that around 800 children and young adults across Europe are thought to be affected by narcolepsy following vaccination.