A British Transport Police spokesman said some of London's mainline stations were closed.
"Waterloo, Victoria, Charing Cross, London Bridge are all closed because there are no trains and no power. There are trains trapped in Underground tunnels. But we have police at most locations."
No injuries have been reported so far. "It's obviously a wider problem than a local power problem," the police spokesman said.
A London underground railway system spokesman said the majority of the network has been affected.
"Trains in stations are being evacuated. We're trying to get alternative power sources started," he added. He blamed a National Grid power failure for the disruption.
But a spokesman for London Energy, which supplies the British capital, said: "We have no information about this at the moment."
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.