The NHS's North West London trust has recommended four A&E departments be closed.
The units in Ealing, Central Middlesex, Charing Cross and Hammersmith could be downgraded to 24/7 urgent care centres.
The new proposed plans would see other major hospitals take A&E patients, peforming both emergency and elective operations, as well as running tensive care units, psychiatric liaison, inpatient paediatrics and a maternity unit.
The hospitals tasked with taking on the extra burden are Chelsea and Westminster, Hillingdon, Northwick Park, St Mary's and West Middlesex.
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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.