More than 13,000 homes in Kent, Sussex and Surrey were left without power after storms lashed the region.
The crew was evacuated from the barge before it broke its moorings
Fallen trees brought down power lines and Seeboard said it had drafted in dozens of engineers as part of its emergency plan to restore supplies.
Earlier a drilling platform anchored off the Kent coast broke its moorings and washed ashore at Cliftonville.
Dover Coastguard said the bad weather caused the barge anchored off Foreness Point to break up at about 0700 BST.
Seeboard spokeswoman Claire Byrd said: "The bad weather really started to cause problems from about 1100 BST on Wednesday.
"We put our emergency plan in place yesterday due to the forecasts and extra staff have been brought in.
"So far we have restored power to 6,000 customers, but earlier this afternoon another 13,700 were without power."
She said they were expecting the worst of the weather to be over by 1900 BST.
The coastguard said no-one was injured in the incident with barge which was carrying out survey work for Southern Water.
The company said the barge, owned by Howard Marine Services in Devon, was involved in research being carried out for a proposed waste water treatment works at Foreness Point.
It became unmoored when the barge platform came off its three-tonne legs.
The crew had been warned about the impending bad weather and had already been evacuated from the barge by the time it broke away.
Meanwhile, two people had to be rescued from their 14ft dinghy when it capsized in strong winds further round the coast in West Sussex.
The crew of the Wanderer dialled 999 as they sat on the hull of the overturned boat close to Chichester Harbour.
The local inshore lifeboat, pulled the pair, who were not injured, to safety.
Solent Coastguard said people were generally heeding the warnings about the weather and staying off the sea.
And in London, the rain and gales caused Hampton Court Flower Show to shut on its third day.