The shop was given listed status because of its historical interest. The Heritage Minister, Ed Vaizey, says it embodies the standard features of the London eel, pie and mash shop, from the gilt lettering on the shop-front to the white-tiled interior with mirrors, seating booths and marble counters.
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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.