The Department for Transport had said: "Today's (Friday) power outage has had knock on impacts on travel".
Thameslink said most of its trains were now at a standstill between London and Bedford.
Experts believe the disconnection of a gas-fired power plant and wind farm triggered the power cut that brought wide-spread disruption to the country on Friday.
A spokeswoman for Northern Powergrid, which serves Yorkshire and the north-east, said 110,000 customers lost power, while at least 26,000 people were without power in the north-west, Electricity North West said.
Keith Bell, a professor of electronic and electrical engineering at the University of Strathclyde, said the power cut was a "relatively small event" compared to blackouts seen elsewhere around the world.
The power outage happened during the Friday evening rush-hour commute.
"We are already very confident that there was no malicious intent or cyber attack involved", National Grid director of operations Duncan Burt told the BBC on Saturday.
He said alarms were also set off by the temporary outage and traffic lights stopped working entirely.
Western Power Distribution said it was working on the issue and expects to have power restored by 6.30pm.
The UK energy watchdog, the Office of Gas and Electricity Markets (Ofgem), is demanding explanations from the National Grid after a major power outage on Friday cut electricity to nearly 1 million people in England and Wales, putting many of them in danger. Ipswich Hospital said it was being affected by the power cut in that area, as its back-up generator had failed to work.
National Grid says its automated systems kick in to stop any damage, chiefly by cutting off parts of the grid to reduce overall demand.
Train services in and out of London, including Thameslink, Southern and Gatwick Express were facing delays and cancellations.
The power failure came as heavy rainstorms drenched the London area, causing flooding at Luton Airport, around 47 kilometres north of the capital. "This has prevented our trains between Farringdon and Bedford from being able to take power and as a result, most of our trains are now at a stand".
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