More than 100,000 London-bound rail commuters - a fifth of the overall total - have to stand at the busiest times of the morning rush-hour, according to Government figures.
Passengers on some morning and evening peak services are travelling on trains which are 60% over capacity on certain routes, the Department for Transport (DfT) figures showed.
More top news
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.