Energy Secretary Kwasi Kwarteng has said that it is “totally unacceptable” that some people are still without power more than a week after Storm Arwen.
It comes as the Energy Networks Association (ENA) said that 4,025 homes were still waiting to be reconnected as of 8am on Sunday. This is down from 4,700 homes on Saturday night.
The majority of the impacted homes are in the north-east of England, the ENA added.
Mr Kwarteng visited Durham to survey the damage done by the storm.
Speaking to the BBC, he said: “I completely accept that this is totally unacceptable.
“It’s wrong and bad for people to be off power for such a long time.
“That’s why I’m here to make sure that we can get people back on as quickly as possible.
“As I’ve said, for 99.5% of people they’re back on, but for the ones that are still having to put up with this is is unacceptable.”
He added that a review will be carried out, and if energy firms are found to have failed to invest in infrastructure then “there could be enforcement action”.
It comes as weather warnings are in place for much of the UK on Tuesday.
Yellow wind weather warnings are in place across England, Wales, and Northern Ireland, with yellow snow warnings in place in Southern and Western Scotland.
On Saturday, gusts of between 35-50 miles per hour battered the country overnight, with temperatures plummeting to below zero in parts of Scotland.
As well as weather warnings, the Met Office predicts further wet and windy weather heading into next week, with poor weather conditions continuing in areas already impacted by Storm Arwen.
Met Office meteorologist Rachel Ayers said: “It will be a relatively nice day today, but overnight tonight it will be windy.
“Temperatures, with the wind and cloud cover, should stay up tonight.
“That should help things a little bit, but we are expecting some more changeable and unsettled weather.
“This unsettled weather isn’t going to help areas that have been impacted by Storm Arwen too much.”
Stewart Sexton, from Alnwick in Northumberland, is on day 10 without power.
“Yesterday we had confirmation that it would be on by close of play today,” the 57-year-old told the PA news agency.
“NPG (Northern Powergrid) even called us back to say yes, confirmed, back on the fifth.
“However, it’s blowing 40mph with rain here today so that confirmation is highly unlikely, if not impossible.”
The Ministry of Defence told PA that 297 personnel from the British Army and Royal Marines were still providing support to civil authorities and conducting door-to-door checks on vulnerable people on Sunday morning.
On Saturday, Boris Johnson said he had held calls with those leading the response to Storm Arwen and the Government is ready to further support the recovery work “in any way we can”.
The long delays have prompted energy regulator Ofgem to warn it will take enforcement action against network companies which failed to restore power to customers quickly enough.
It has also agreed with firms to lift the £700 cap on compensation which 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, are an initial £70 for the first 48 hours’ of any cut.