Daljit Lally, chief executive of Northumberland County Council, has also called for more support after a major incident was declared there.
Residents in affected areas have told how they have been struggling to cope over the past week.
Jessica Teasdale, 35, from Stanley, told the PA news agency: “People are frustrated and angry. Everyone is getting ill.”
Ms Teasdale’s partner, Christopher Bertram, 39, said: “I am sitting looking at Jessica now and she is a wreck. She hasn’t slept or washed properly for a week. She’s like a shell of a person. It is awful to watch.
“I’m using my dog as a hot water bottle.”
Helen Shand, who lives in Inchmarlo, Aberdeenshire, was left without electricity, and made the decision to go to her son’s house in a nearby village after a few days because of the outage.
She said: “It was miserable. I have never been so cold in all my life, even the dog was cold.”
Northern Powergrid, the electricity distribution network operator for the North East, Yorkshire and North Lincolnshire, said 6,000 customers remained off supply at 11pm on Thursday. Power has been restored to 234,000 others since Storm Arwen swept across the country on Friday, November 26.
SSEN said it expects to restore power to 1,100 homes throughout the course of Friday and into the evening. Another 500 customers are expected to be reconnected throughout the course of Saturday.
A spokesman said: “SSEN welcomes Ofgem’s review into Storm Arwen. Our focus remains firmly on reconnecting the remaining customers without power, and we will also be conducting our own internal review.”