South West Trains are promising that commuter services will be "normal" in the morning, following hours of delays due to engineering work.
In a statement, the company said: "Safety is our absolute priority. We have no choice but to make sure these repairs are carried out before we can restore train services on these lines."
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.