The second major storm of the winter - named Barra by the Irish Met Office - is set to batter the UK on Tuesday.
Weather warnings have been issued for wind and snow as thousands of homes are still without power nine days after Storm Arwen.
Forecasters say the further bad weather may hinder efforts to reconnect properties.
Energy Secretary Kwasi Kwarteng said it was "totally unacceptable" that thousands of homes remain without power, after Labour claimed the government would have taken the problem more seriously if the South East had been affected.
Speaking during a visit to Durham, Mr Kwarteng said: "I feel that we've engaged with this problem right from the start of the week.
"We have got 99.5% of the people who were affected back on the power supply. For the 0.5%, that's no solace at all...but it's wrong to say nothing has been done."
Mr Kwarteng 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".
'This wouldn't happen in London or Surrey'
Shadow environment secretary Jim McMahon said it "beggars belief" that the loss of power to so many homes has been not been considered a "national priority".
He told Sky News' Trevor Phillips on Sunday programme: "I firmly believe had this been the case where 20,000 properties were without power in Surrey or in London, the government would absolutely have treated it with more seriousness.
"For people in County Durham who I spoke to, they felt isolated, they felt angry and they felt forgotten."
Storm Barra, which is forecast to bring snow and winds in excess of 70mph on Tuesday and Wednesday, has been named for its potential impact on Ireland.
However fresh warnings for high winds have been issued across the UK for Tuesday and could mean more power supply problems and disruption to transport, the Met Office said.
A warning for snow on the same day covers the North of England and Scotland. Again the Met Office says there is a chance of power outages and a "slight chance" rural communities could be cut off.
Heavy rainfall yesterday meant hundreds of properties that had power restored were again without supply in Northumberland, a local councillor told Sky News.
Latest data showed 3,190 homes were without power across northern England and Scotland on Sunday afternoon, down from 4,025 homes on Sunday morning, according to industry body the Energy Networks Association.
An 'absence of government leadership'
Ed Miliband, the shadow climate change secretary, said it was "completely outrageous" that thousands of people have been without power for more than a week, after Storm Arwen hit on 26 November.
"People are being left in the most appalling circumstances and there has been an absence of government leadership," Mr Miliband said.
"We need an urgent investigation to understand what went wrong, and to ensure that our power systems are never again this vulnerable to extreme weather events."
PM 'concerned' about prolonged power outages
Boris Johnson expressed concern at the number of homes still without power as he held calls with local leaders and Lt Col Mark Steed, who is coordinating the military involvement in the response.
The prime minister tweeted: "I am grateful for the tireless efforts of the emergency teams and volunteers on the ground but remain concerned that... households are still without power.
"I reiterated to those I spoke to that the government is ready to further support their work in any way we can."
Steven Bridgett, a councillor in Rothbury in Northumberland, said about 150 properties in the area were without power on Saturday but the number had soared again after "significant rainfall and wind" overnight.
"That pretty much wiped out all of the good work that had been achieved over the last three or four days," he told Sky News.
"We're now back up to about 600 properties that are still without power.
"We've got significant surface water flooding happening in this area as well. Some of the roads are starting to flood.
"We've pretty much had constant rainfall now for 12 to 14 hours.
"It started off as snow then it progressed into heavy rainfall with wind."
Mr Bridgett praised the response from the local council and emergency services but believes a "major incident" should have been declared earlier.
He said essentials including water, batteries and logs were available for affected residents at collection points in Rothbury and Whittingham.
"We've had significant flooding, we've had significant winter storms, we've had a week with no gas - we are a pretty tough and resilient community in this area," Mr Bridgett added.
Weather warnings issued
With work still ongoing to restore power, forecasters predict low temperatures of between 4C (39F) and 6C (43F) accompanied by some gale-force winds for the region over the coming days.
A band of rain and snow is expected on Monday, along with more wind.
From Tuesday, the UK is set to see continued wind, rain, and snow, with a likelihood of more strong gusts, although not as strong as Arwen, into Wednesday.
Simon Partridge, a meteorologist at the Met Office, said the expected weather conditions were "not helpful" for the work to reconnect power supplies and get to remote areas.
"It's certainly not ideal, and the higher locations certainly will be seeing some more snow in the coming days," he added.
Energy regulator Ofgem has warned it will take enforcement action against network companies which failed to restore power to customers quickly enough following the storm.
It has also agreed with firms to lift the £700 cap on compensation which could be given to customers.
The change will allow those affected to claim £70 for each 12-hour period they are left without power, after an initial £70 for the first 48 hours.
Nearly 300 military personnel from the British Army and Royal Marines were deployed to offer support and were conducting door-to-door checks on vulnerable people in their homes.