The cut hit transport services across the British capital, causing travel chaos for thousands who had to abandon trains and take to the streets.
Many were trapped in underground trains.
"There was a fault on a transformer system. There was loss of power for 34 minutes, but London Electricity has re-energised the system and it's back on," an Ofgem spokesman said.
But a spokesman for London Energy which supplies the British capital, was unable to comment on reasons for the power failure, saying: "We have no information about this at the moment."
Rail worst hit
In scenes reminiscent of the blackout that hit North America earlier this month, a British Transport Police spokesman said some of London's mainline stations had to close.
"Waterloo, Victoria, Charing Cross, London Bridge [railway stations] are all closed because there are no trains and no power … we have police at most locations," the spokesman said. No injuries were reported at any of these locations.
A London underground railway system spokesman said the majority of the network has been affected, blaming a National Grid power failure for the disruption.
Earlier this month, one of the largest power outages in North American history blacked out New York and other major US and Canadian cities overnight, disrupting life for millions of people and trapping thousands in lifts and on crowded subways.