In addition to the problems out of Euston station, there are also problems at King's Cross. East Coast is advising customers out of King's Cross not to attempt to travel on its services north of Newcastle.
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Mayor of London Sadiq Khan is backing the scheme.
A spokesperson said the lightning strikes had left the "aircraft fuelling system unavailable."
Nearly 1,000 properties have been left without power, and road users have been warned of potentially hazardous conditions.