Thousands of homes and businesses across Norfolk, Suffolk and Essex are still without electricity after the major storms on Thursday.
EDF Energy said the storm caused so much damage to the electricity network it was similar to having more than one month of faults all in one go.
As of Sunday morning 5,700 were still without power across the region.
The company said hundreds of engineers were working and most people were due to have power by the end of Sunday.
A spokesperson for EDF said: "Many customers who are still without power will be reconnected during Sunday.
"However, some final reconnections may not take place until early next week."
Engineers from EDF's parent company in France have also been drafted in to cope with the electricity supply problems.
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