Strong winds are expected to sweep across the Republic of Ireland on Tuesday, with gusts reaching up to 110kph in exposed coastal areas.
Blustery winds and rain, later turning to snow, are also forecast for northern England and Scotland.
A rare red alert was issued for the counties of Cork and Kerry in the Republic of Ireland before Storm Barra hits. The Met Office has issued yellow national severe weather warnings for wind and snow for most of the UK.
There are warnings of dangerous coastal waves, atrocious driving conditions, travel delays, flooding and damage to buildings when Storm Barra sweeps across.
Forecasters warn of heavy rain in the south of England and sleet and snow in the north and into Scotland. Blizzards and snowfall as deep as 20 centimetres are expected at higher levels.
“A band of rain will turn to snow across northern England and Scotland through Tuesday,” said Brent Walker, deputy chief meteorologist at the Met Office.
"Two to five centimetres of snow is expected to accumulate quite widely across the warning area.
“Strong south-easterly winds will also lead to snow drifting in places, particularly over the highest routes, adding to poor visibilities."
When the storm lands on the western coasts of England and Wales it will also coincide with high tides.
Storm Barra is not expected to be as strong as Arwen, which late last month brought gusts up to 160kph that led to the worst damage to the electricity network in a generation and power cuts for more than a million homes.
British Prime Minister Boris Johnson said on Monday that homes still without power after Storm Arwen will be reconnected “by tomorrow at the latest”.
Mr 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 were still cut off on Monday.
After a call with the president and chief executive of Northern Powergrid, Phil Jones, Mr Johnson said he “was assured they would be reconnected tomorrow at the latest”.
British Energy Minister Greg Hands responded to a question in the Commons on the power cuts that 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”.
“I’m glad to say that 99.8 per cent of those affected by the storm have had their power supply restored so far," said Mr Hands, who is also the Conservative MP for Chelsea and Fulham.
“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.
“I have been assured by the network operators that all efforts are focused on having power restored to those households in the next day."
Labour's Kevan Jones, who asked the 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."
Ed Miliband, the shadow climate change minister, quoted a Conservative councillor from northern England as saying: “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, the Member for Doncaster North, said Business Secretary Kwasi Kwarteng was “available for a photo opportunity” at the weekend as he visited areas affected by the storm, but 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.
“It’s exhausting, it’s wearing us down and it’s a constant worry. Every day seems to bring a new problem,” Mr Sexton said.
“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 sewerage 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 20 kilometres to his sister’s home.
He said his village 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 occasionally at 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”, Mr Sexton said.
Another Alnwick resident, Anna Elson, 49, also said she was travelling to a family member’s house with her son, 13, for a hot meal and a shower.
Ms Elson said she and her son suffered from rheumatoid arthritis, a condition worsened by the cold.
“The village was left to cope on its own for too long," she said. "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, but we are fed up and angry at the lack of response we have had.”
Scottish and Southern Electricity Networks said power had been restored to all 135,000 of its affected customers by Sunday.
Mr 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, he said he believed the power grid system could be made “a lot more resilient”.
“We will have a review," Mr Kwarteng said. "We will see if the distributor companies have enough infrastructure. We may even have enforcement action if necessary."
The long delays have prompted energy regulator Ofgem to warn that it will take enforcement action against network companies that failed to restore power to customers quickly enough.
It has also agreed with companies 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.