A £700 cap on compensation has also been lifted.
Regulator Ofgem has launched an “urgent” review into the response of energy network companies to Storm Arwen which has left some people without power for a week.
A £700 cap on compensation has also been lifted, allowing those affected to claim £70 for each 12-hour period they are left without power, after an initial £70 for the first 48 hours.
Ofgem said that around 10,500 people are still without power in some parts of Scotland and the North of England.
The regulator said its review will establish the facts about the response and if necessary it will pursue further enforcement action.
Jonathan Brearley, Ofgem’s chief executive, said: “We understand this is a really worrying time for people who are without heat and power as the severity of Storm Arwen has hit homes and businesses in the North of England and Scotland. The effects of Storm Arwen are still being felt with 10,500 homes still without power.
“We accept the network companies have been working in challenging conditions, but until every home in Britain has power restored, that relentless effort must continue.
“We are launching a review into how the storm has been handled. We have strict rules on how network companies need to operate in these circumstances and we will take action if needed.”
He added: “I’ve launched an urgent review to see if there are things that the industry could learn from this response in order to improve our support to consumers in the future.”
The review will focus on the role of the network companies in maintaining the resilience of the system and their emergency response, including their communications with customers.
Around 130 troops have been sent to carry out door-to-door checks and offer welfare support in north-east of Scotland, where around 1,600 Scottish and Southern Electricity Networks (SSEN) customers remained off supply at 10am on Friday.
South of the border, Durham County Council said around 100 servicemen and women will be based in Weardale to help local people.
A major incident has also been declared in Northumberland as a result of the weather, with chief executive of Northumberland County Council Daljit Lally calling for more support to the emergency services to help residents.
Details of what additional support will be available is due to be discussed later.
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.
“I saw my elderly neighbour yesterday, the poor man looked like he was going to cry. He’s a vulnerable person but no-one has checked on him and he lives alone.”
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 northern Lincolnshire, said 6,000 customers remained off supply at 11pm on Thursday, though 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 and around 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.”