Another named storm is expected to bring “severe and damaging gusts” on Tuesday after two people died as a result of Storm Isha.
An 84-year-old man died after the car he was travelling in crashed into a fallen tree in Grangemouth, Scotland.
In Limavady, Co Londonderry, a man in his 60s died after a crash involving two vans and another fallen tree.
Winds measuring almost 100mph brought disruption for many during Storm Isha.
In the Yorkshire Dales, a number of people were rescued from four trapped vehicles in Morton-on-Swale by firefighters.
One woman retrieved from a flooded road, Charlie Curry, said it was a “terrifying experience”.
“But I made it out alive and everyone’s alright,” she told ITV Calendar News.
It followed a similar incident in Appersett.
Storm Jocelyn, which is due to bring intense conditions from 6pm on Tuesday, has been named by Ireland’s meteorological service.
Met Eireann described it as a “mature low pressure system [that] will bring very strong southwest to west winds with severe and damaging gusts”.
Jocelyn – the 10th named storm in five months – is not expected to hit the entire UK with the same impact as Storm Isha.
It will, however, affect the weather here. The Met Office has an amber weather warning for wind in place for western and northern Scotland.
It starts at 6pm on Tuesday and continues until 8am on Wednesday.
There is a “good chance” of power cuts and “probably some damage to buildings”, the Met Office said.
ScotRail services across Scotland will be suspended from 7pm on Tuesday and there will be no rush hour services the following morning.
“It will not be safe for our customers and our staff,” said Phil Campbell, ScotRail’s customer operations director.
“This is the second withdrawal of train services this week, and we know the impact this has on customers, but the safety of staff and passengers will always be our priority.”
There are yellow warnings for wind in place across much of the UK north of Oxford and Peterborough from Tuesday afternoon, and for rain in an area of western Scotland stretching from the border with England to near Inverness.
There is also a warning for rain in Cumbria.
Met Eireann has also issued amber wind warnings for parts of west and northwest Ireland tomorrow evening.
Following Storm Isha, transport services largely recovered on Monday, although some roads remained closed and railway lines were blocked.
Dozens of schools asked parents to keep their children at home.
About 20,000 passengers were affected by almost 150 flight cancellations at Dublin Airport on Sunday, and the travel headaches continued on Monday.
At noon on Monday, Northern Ireland Electricity Networks said 24,000 customers remained without power because of the storm.
There were also power cuts affecting thousands of people in northwest England.