Storm Jocelyn has hit the UK with 71mph gusts, with major disruption to transport services expected.
The storm is expected to be at its worst in the early hours of Wednesday – with a possibility that weather warnings are extended, the Met Office said.
It comes after eight flights were cancelled at Dublin airport and four at Glasgow airport on Tuesday evening, train services in Scotland were suspended from 7pm and drivers were warned to postpone journeys and not to park near trees.
The strongest winds of up to 80mph are expected between 3am and 7am on Wednesday, before the storm eases off throughout the day.
Jocelyn comes barely two days after Storm Isha left two people dead and one seriously injured, while thousands of people remained flooded and without power.
A yellow warning for ice has also been issued across northern and eastern parts of Scotland, while 80mph gusts could hit exposed areas, the forecaster said.
Avanti West Coast was among the train providers warning members of the public that they would not be able to travel by rail in large parts of the north of England.
The train services affected would be closed until at least midday on Wednesday, the companies said, and passengers with tickets who could not travel could get a full refund.
Jocelyn continues what has been the most active storm season in the UK and Ireland since records began.
About 4,900 people were still without power in Britain on Tuesday morning, mainly in the north of England and the south of Scotland, the Energy Networks Association said. In Northern Ireland, about 7,000 customers were without power.
The stormy weather also led to higher river and lake levels across the UK. In England on Tuesday the Environment Agency had 13 flood warnings in place, indicating that flooding was expected and people needed to take immediate action. They included the River Lambourn in Berkshire, Derwent Water in the Lake District and the River Ouse in York.
There were also 82 flood alerts in place in England, which urge people to “be prepared” as flooding is possible. In Scotland, there were 15 flood warnings and 10 flood alerts.
Isha led to at least two deaths in the UK. An 84-year-old man died after a car in which he was a passenger crashed into a fallen tree in Grangemouth, Falkirk.
A man in his 60s was killed in a crash involving two vans and a fallen tree in Limavady, Co Londonderry, on Sunday night.
A 26-year-old man was in a critical condition after his car hit a tree on a road in Cramlington, Northumberland, police said.
A man in his 60s and a woman in her 50s were seriously injured in Somerset on Sunday evening after a car either collided with a fallen tree or was struck by it as it fell.
The woman’s condition was described as life-threatening, while the man’s injury was potentially life-changing, Avon and Somerset constabulary said as they appealed for witnesses.
In Bradford, a man died on Monday after reportedly falling into a maintenance hole at roadworks. One line of inquiry is that strong winds blew barriers away.