National Rail said trains between Ashington and Newcastle would not call at Northumberland Park, while services from Newcastle to Ashington would not stop at Blyth Bebside.
Electricity North West offered 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 could 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, because of strong winds – a section of road nearly 15 miles 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.
A yellow wind warning was issued in Cumbria, to apply from 18:00 GMT on Monday.
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