Thousands of people are still without power and the Army has been deployed to help residents in areas which have suffered most from Storm Arwen.
Troops will conduct door-to-door checks on more than 4,000 homes, and provide welfare support for remote communities.
Mr Johnson said: “It was a very, very big storm. We are doing everything we can to to help people.
“There were about 19,000 homes without (power) this morning. We have got that down to about 16,000.
“That is no consolation for the 16,000 who are still suffering but we are working flat out to help you.”
Troops are also being sent to the north east of England which has also suffered damage from the storm.
The Department for Business, Energy and Industrial Strategy (BEIS) said almost a million households have been affected by power cuts over the past week, but electricity has been restored to 960,000 homes.
Scottish and Southern Electricity Networks (SSEN), which distributes power to 3.7 million homes in central southern England and the north of Scotland, said the worst-affected areas include Aberdeen Aberdeenshire, Moray, Angus, Perthshire and Stirlingshire.
It aims to restore power to all homes in the regions by the end of Friday.
People who are without power and are unable to stay with families or friends can get costs reimbursed from SSEN for other accommodation.
Durham County Council has declared a major incident, and up to 13,000 properties in areas including Teesdale and Weardale are still without power.
Over the past few days, representatives from the council, Durham and County Darlington Fire and Rescue Service, Durham Constabulary, the Mountain Rescue Service, Northumbrian Water and Northern Powergrid have been providing information on the support available, along with bottled water and phone-charging points.
Conservative MP for North West Durham Richard Holden said he had spoken to defence minister James Heappey who had confirmed around 100 troops are being deployed to the area “and will be on the ground in north east England from tomorrow”.
More rain, sleet and snow fell in south-western parts of the UK on Thursday, while wintry showers have affected the North and East.
The Met Office said the showers will be confined to Norfolk later on Thursday, with gales easing along the North Sea coast.
More snow is expected to hit Scotland on Friday before moving towards the South East, and rain is predicted for north-western parts.
Eastern parts of Scotland are predicted to have highs of 2C (35.6F) while western Scotland could reach 4C (39.2F).
Across England there may be highs of 3C (37.4F) and 4C on Thursday, with some sunny spells and cloud later.
Clare Pennington, from Newtyle in Angus, is facing her sixth day without power and is staying in a static home as she is building a house.
The project manager in sustainability told the PA news agency: “It has been as cold inside as it is outside and I’ve had no heating, hot water or light since Friday.
“(We feel) totally forgotten (about). It was freezing last night, too cold to sleep.
“It’s really cold and damp and while I’ve not had an asthma attack for years, I can feel my breath getting wheezy as well as a cough.
“I think what is so frustrating is the continued excuse of (the weather being) unprecedented.
“It may be unprecedented but it’s been predicted by climate scientists for years and it’s only set to get worse, but our electricity infrastructure is aging and wholly unprepared.”
Labour’s shadow environment secretary Jim McMahon said: “Thousands have been left without power for days on end, especially in rural and more remote communities, yet they have been mostly abandoned by the Government.
“Half-hearted reassurance from ministers hundreds of miles away is completely useless when so many people are unable to cook, charge their phones or store vital medicines properly.
“The Conservatives need to get their act together and ensure there is resilient infrastructure across the country to stand up to the more severe storms we know are coming in the climate crisis.”
The Energy Networks Association said it aims to reconnect most homes by Friday.
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