Storms Malik and Corrie left around 40,000 homes in Scotland and 7,000 in northern England without power.
On Saturday, two people were killed by falling trees – a boy in Staffordshire and a woman in Aberdeen.
Several schools in Aberdeenshire were closed on Monday due to storm damage or power outages.
Much of Scotland, Northern Ireland and parts of northern England was under a yellow Met Office warning for wind over the weekend.
Gusts of 92mph were recorded on Sunday night at Stornoway in the Western Isles.
But the Met Office said the next few days would be much calmer before a brief cold snap on Thursday.
Scottish and Southern Electricity Networks (SSEN) said it had restored power to around 68,000 customers affected by Storm Malik but 7,000 still remained without power, while a further 33,000 were without power as a result of Storm Corrie.
SSEN said it was prioritising the 7,000 customers still without power after Storm Malik – mainly in Aberdeenshire – and it hoped the vast majority would have electricity restored on Monday, with full supply returned by Tuesday evening.
In England, Northern Powergrid said 80,000 customers had been affected by Storm Malik, with around 4,000 remaining without power, while Storm Corrie had affected at least 3,000 customers beyond that.
While the company said some restoration work may run into Tuesday, director of field operations Andy Bilclough said the team was “shooting to get it all done today”