Storm Jocelyn will thrash the UK with more wind and rain after Storm Isha left two people dead and one seriously injured.
Another weather system will bring windy weather on Tuesday night and into Wednesday for much of the northern half of the country, The Met Office said.
Amber and yellow weather warnings for wind have been issued covering much of the UK, together with yellow warnings for rain covering parts of western and southern Scotland, and north-west England.
A yellow warning for ice has also been issued across northern and eastern parts of Scotland.
Gusts of 80mph could be experienced in exposed areas, with 40-50mm of rain possible over higher ground, the forecaster said.
Met Office chief meteorologist Steve Willington said Storm Jocelyn, named by Met Eireann, could cause further disruption hot on the heels of Storm Isha.
He said: “Although this system will be a step down relative to Storm Isha, with the damage and clean up still underway, we could potentially see more impacts from Storm Jocelyn.
“Outbreaks of heavy rain on Tuesday could bring rainfall accumulations of 15 to 20mm quite widely with 40 to 50mm over higher ground in southwest Scotland, the Scottish Highlands and parts of northwest England.
“Wind gusts are expected to reach 55 to 65mph across northwestern Scotland while there is potential for winds to gust to reach 75 to 80mph in a few places, in particular exposed parts of the Western Isles and coastal northwest Scotland early on Wednesday morning.”
Met Office spokesman Stephen Dixon said Tuesday will be another wet day before windspeeds start to pick up towards the evening.
“Tuesday will be quite a wet day for many people with a rain front bringing the chance of disruption,” he said.
“Higher windspeeds will start to develop overnight on Tuesday into Wednesday morning.
“Windspeeds from Storm Jocelyn will be a slight notch down from Storm Isha, but with the clean up still underway, more disruption is likely.”
Temperatures are expected to remain mild.
Further transport disruption is expected on Tuesday after services had largely recovered on Monday.
ScotRail services across Scotland will be suspended from 7pm and there will be no rush-hour services on Wednesday, the railway operator has said.
Martin Thomson, national operations manager for resilience at Transport Scotland, said: “Across the wider network, we can expect to see more delays and cancellations with ferries, flights and rail from Tuesday into Wednesday morning.”
The Met Office said the highest recorded windspeed during Storm Isha was 99mph at Brizlee Wood in Northumberland, with gusts of 90mph at Capel Curig in Snowdonia on Sunday.
A 26-year-old man was in a critical condition on Monday night after his car hit a tree on a road in Northumberland, police said.
An 84-year-old man died after the car in which he was a front seat passenger crashed into a fallen tree in Grangemouth, Falkirk, Police Scotland said.
And a man in his 60s was killed in a crash involving two vans and a fallen tree in Limavady, Co Londonderry, on Sunday night, the Police Service of Northern Ireland said.
Many people were expected to spend Monday night without any power, The Energy Networks Association said.
Some 24,000 were without power in some parts of Great Britain on Monday evening, mainly in the north of England and in Scotland.
In Northern Ireland, 15,000 customers were without power.
A number of people were rescued by firefighters from flooded roads in the Yorkshire Dales.
A Network Rail spokesman said “hundreds of engineers” were deployed with chainsaws and cherry pickers to remove debris from tracks.
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