Homes still without power following Storm Arwen will be reconnected “by tomorrow at the latest”, the Prime Minister has said.
Boris Johnson said he spoke to the chief executive of Northern Powergrid on Monday, and that he had been told of the new target.
But a deadline set on Wednesday last week had already been missed as MPs heard there was something “seriously wrong” at the supplier.
On Wednesday, Downing Street said properties affected by the power cuts caused by Storm Arwen should have supply restored “by the end of the week”, but more than 1,000 remained cut off on Monday.
Earlier in the day, the energy minister, Greg Hands, said it was “completely unacceptable” that around 1,600 households were still without power.
Following a call with the boss of Northern Powergrid, Phil Jones, Mr Johnson said he “was assured they (affected properties) would be reconnected tomorrow at the latest”.
He said on Twitter: “I also asked for assurances that the energy supply companies were putting in place measures to limit any potential further disruption to households as a result of Storm Barra.”
Mr Hands responded to an urgent question in the Commons on the power outages that have affected some residents in the north-east for 10 days, while Storm Barra threatens to cause more chaos on Tuesday.
Labour has also accused the Government of treating people in Scotland and the north of England as “second-class citizens”.
Mr Hands, who is also the Conservative MP for Chelsea and Fulham, said: “I’m glad to say that 99.8% of those affected by the storm have had their power supply restored so far.
“But this is not good enough, it is completely unacceptable that around 1,600 were still in this position as of this morning, but the situation is improving each hour.”
He added: “I have been assured by the network operators that all efforts are focused on having power restored to those households (still without power) in the next day.”
Labour’s Kevan Jones, who brought the urgent question, said: “There is something seriously wrong with Northern Powergrid, not with the engineers and individuals who are out restoring power, but with the management and senior management of that company.”
Quoting a Conservative councillor from northern England, the shadow climate change minister, Ed Miliband, said: “‘If this happened in London or in the south-east everything would have got thrown at it’. They are his words. Aren’t people in the north entitled to think he is right? They have been treated as second-class citizens.”
Mr Miliband, MP for Doncaster North, added that the Business Secretary, Kwasi Kwarteng, was “available for a photo opportunity” at the weekend as he visited areas affected by the storm, but had allowed Mr Hands, one of his ministers, to face questions about the power cuts in the Commons.
Residents in the north-east of England have spoken of losing hope and feeling “fed up and angry” as they face an 11th night without power.
Stewart Sexton, 57, who lives in Alnwick, Northumberland, with his partner, said Northern Powergrid had promised their power would be restored within 24 hours every day since it was cut off on November 26.
He told the PA news agency: “It’s exhausting, it’s wearing us down, and it’s a constant worry. Every day seems to bring a new problem.
“On day nine there was torrential rain and our village started to flood. That was mainly because of the storm debris.
“What happened was that then flooded our village water works – it flooded our sewage system. Our neighbour couldn’t use his toilet without it flooding.
“I had to clear standing water from the road, which got my clothes wet, and then return to a house without heating.
“From my window I can see a snapped telegraph pole and cables lying on the ground.
“The weather forecast is dreadful. We have not got any hope at all. It’s awful, it’s the futility of it.”
Mr Sexton said he had been showering using water heated on a wood-burning stove in his living room, and by travelling 12 miles to his sister’s home.
He said his village had had little support, with no sign of reinforcements from the Army, fire service or council, and their main form of sustenance had been from a van providing free fish and chips at sporadic times over the weekend.
Northern Powergrid has handed out survival packs consisting of a small blanket, hot-water bottle, mug, pair of socks, glove and hat – but “no logs, candles or batteries”, he added.
Another Alnwick resident, Anna Elson, 49, also said she was travelling to a family member’s house with her 13-year-old son for a hot meal and a shower.
She told the PA news agency that both she and her son suffered from rheumatoid arthritis, a condition worsened by the cold.
Ms Elson said: “The village was left to cope on its own for too long, there are a few medically vulnerable residents here, including me.
“No phone signal doesn’t help and makes us feel more vulnerable. Help has started to come but people feel it should have been a lot sooner.
“Friends have offered help and the village has come together,” she added.
“But we are fed up and angry at the lack of response we have had.”
Scottish and Southern Electricity Networks (SSEN) said power had been restored to all 135,000 of its affected customers by Sunday.
Storm Barra will hit on Tuesday, the Met Office has warned.
While the west of Ireland will receive the worst of the storm, yellow wind weather warnings are in place across England, Wales and Northern Ireland.
Yellow snow warnings are also in place in southern and western Scotland.
The Met Office has warned that gale-force winds of 45-50mph on Tuesday could make it more difficult for engineers to reconnect homes, but spokesman Stephen Dixon said that winds would “gradually weaken” as they move east and should have petered out by Thursday.
Energy Secretary Kwasi Kwarteng visited the north-east on Sunday to see the damage done by the storm.
During a visit to a Northern Powergrid call centre in Penshaw, near Sunderland, Mr Kwarteng told the PA news agency he believed the power grid system could be made “a lot more resilient”.
“We will have a review, we will see if the distributor companies have enough infrastructure, we may even have enforcement action if necessary,” he added.
The long delays have prompted energy regulator Ofgem to warn it will take enforcement action against network companies that failed to restore power to customers quickly enough.
It has also agreed with firms to lift the £700 cap on compensation that could be offered to those stuck without power.
The change will allow those affected to claim £70 for each 12-hour period they have no electricity, after an initial £70 for the first 48 hours of any cut.
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