Electricity North West said it was offering free welfare support to residents at Cartmel Food Shed Takeaway until 14:00 GMT, as well as at locations in Ulverston and Askam-in-Furness.
Paul Killilea, of Electricity North West, said the majority of homes affected should have their power restored on Monday, but hundreds of homes may remain without power overnight.
“[There is] a significant amount of work to do today,” he said.
The A66 reopened on Sunday evening after it was closed in both directions between the A67 near Bowes in County Durham and the A685 near Brough, Cumbria, due to strong winds – a section of road nearly 15 miles (24 km) long.
The Redheugh Bridge was shut on Sunday afternoon due to high winds but was later reopened.
The Shields Ferry is running following its cancellation on Sunday.
No severe weather warnings remain in place across the North East or Cumbria on Monday, but a yellow wind warning has been issued in Cumbria for Tuesday.
Follow BBC North East on X, external and Facebook, external and BBC Cumbria on X, external and Facebook, external and both on Nextdoor and Instagram, external.