Some 5,000 people were evacuated when police declared a major incident in Kingsway in Holborn on Wednesday.
About 50 firefighters remain at the scene as engineers continue to work to restore power to 400 customers.
Some 3,000 customers, including India House, had originally been without power as a result of the fire, UK Power Networks said.
A spokesperson said: "During the night National Grid were able to stop the flow of gas at Kingsway so the fire could be extinguished, enabling us to continue restoring electricity supplies.
"The cause of the incident is being investigated, but until utilities can access the tunnel it's impossible to determine."
London Fire Brigade (LFB) station manager Sean Madeley said the fire had been put out at about 09:00 BST.
"We're staying at the scene to assist UK Network as they carry out work in the tunnel as a safety precaution," he added.
The London School of Economics (LSE), High Court and Indian High Commission were among nearly 100 businesses affected by the loss of power.
"There is no power or internet in the building. We have a generator so the building has lights," an India House spokesperson said.
Scotland Yard inspector Neil Johnson said: "I imagine this road will be closed a long time after this is finished because of damage the heat does to the road.
"It will have to remain closed until a structural engineer examines it properly and either he or she says what work has to be done and that work is completed - this is not an overnight job."
Several West End theatres were forced to cancel performances on Wednesday evening including Beautiful - The Carole King Musical, Charlie And The Chocolate Factory, Disney's The Lion King, Gypsy, Mamma Mia! The Play That Goes Wrong and The Woman In Black.
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