Crews working for power company Seeboard spent much of last night repairing fallen cables and broken lines.
Sussex was one of the worst-hit areas of Britain and more than 10,000 homes had their power cut off overnight.
Gale force winds today hampered work on overhead lines.
Seeboard spokeswoman Claire Byrd said: "We have been making safety judgements and only carrying out repairs at ground level. It is too dangerous for them to work on overhead lines."
The firm warned people not to go near fallen cables because they could still be live.
Reports of faults to Seeboard should be made by calling 0800 7838866.
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