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Hundreds of properties were left without power after a cable was damaged.
Power was restored to some customers fairly quickly but many, including Gravesham council, were still affected hours later.
A UK Power Networks spokesman said on Monday: "We are investigating a report of cable damage in the area.
"Power was interrupted to 565 customers in the Windmill Street area of Gravesend at 9.31am today.
"Engineers restored supplies to 116 customers at 9.52am and are working quickly and safely to restore remaining supplies."
Gravesham council issued a statement just after 10am saying: "The civic centre currently has no electricity as there has been a power cut in the local area.
"Our telephones are working but we are unable to access information and payments at present.
"We will update you when we are back on line. Sorry for any inconvenience that this may cause."
Remaining supplies were restored at 5.12pm.