Some 16,000 households were still without power in Scotland and north-east England on Sunday evening, after two storms hit the UK at the weekend.
Storms Malik and Corrie have left around 7,000 homes in northern England and 9,000 in Scotland without power.
On Saturday, two people were killed by falling trees – a boy in Staffordshire and a woman in Aberdeen.
A Met Office amber weather warning is in place along the east coast of Scotland until 06:00 GMT.
Several schools in Aberdeenshire said they would shut or delay opening on Monday due to power and heating issues.
Much of Scotland, Northern Ireland and parts of northern England are under a yellow Met Office warning for wind.
Gusts of 92mph were recorded on Sunday night in Stornoway, on the Western Isles.
Deputy First Minister John Swinney said it was likely that more homes would lose power during Storm Corrie on Sunday night, telling BBC Scotland: “We’re in for quite a challenging few days.”
Scottish and Southern Electricity Networks (SSEN) said it had restored power to around 64,000 customers affected by Storm Malik, with the aiming of restoring another 1,500 homes overnight on Sunday.
Ice warnings have been issued for Monday for areas covering Grampian, Highlands and Eilean Siar, Strathclyde and Fife.
In England, Northern Powergrid warned “a relatively small proportion of our customers” living in Northumberland and County Durham would remain without power beyond Sunday night.
A major incident was declared in County Durham after Storm Malik prompted road closures, fallen trees and felled power lines.
Andy Bilclough, Northern Powergrid’s director of field operations, said: “We still have a lot to do but we have a large team out there now in what are currently perfect conditions for the kind of work we do.”
ScotRail said domestic services were being withdrawn from 18:00 GMT on Sunday due to “very strong winds”. A number of Monday’s services have been replaced by buses.
Police in Staffordshire said a 72-year-old man remains in hospital after being hit by a falling tree Winnothdale, near Tean, on Saturday afternoon. A nine-year-old boy died in the same incident.
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