The country is now under amber or yellow alert depending on the area.
Two men were killed by falling trees as Storm Arwen lashes the northern parts of the UK, bringing gusts of wind reaching up to 160km/h.
A man died in Northern Ireland on Friday when his car was hit by a falling tree, police said. Another man died in northeast England when a tree fell on him.
Britain's meteorological agency had placed vast swathes of eastern Scotland and northeastern England on red alert for wind overnight. The country is now under amber or yellow alert depending on the area, but the weather agency still advises people not to travel unless absolutely necessary.
The Met Office forecasts that amber areas could see gusts of wind reaching 120 km/h.
In Scotland, several train lines were disrupted between Edinburgh, Glasgow and other major cities after a wind-blown barn landed on the tracks. Many roads in the worst affected areas of Scotland are also closed due to debris on the tracks.
Around 120 lorries were caught out by the weather and are now "stuck in the snow" on a motorway in the north of England, road police said on Saturday, as they deployed a snow plough to try to resolve the situation.
Energy supplier Northern Powergrid estimates that strong gusts have left 55,000 customers without power in the north of England, including the county of Northumberland, where the town of Brizlee Wood experienced winds of up to 160km/h, according to Met Office records.
Numerous videos posted on social media show howling winds and raging seas across the country.
"People should stay away from the coast as the waves are life-threatening," the Met Office warned on Saturday.