Engineers for Electricity North West have restored power to 17,000 properties across the South Lakes and North Lancashire areas affected by Storm Debi.
Near Kendal a tree fell on a 33,000-volt line but did not cause customers to lose power. Engineers and tree cutters attended site to make the site safe and remove the tree.
Winds have hit 70mph in some areas today making it unsafe for overhead lines teams to climb and make repairs.
Mark Mercer said: "We have had 46 individual damages on the network today, largely caused by trees and windborne debris hitting the overhead line network.
"Our teams have made good progress with repairs despite the continuing challenges of the high winds and remain out on the network restoring power to the 2,500 or so properties remaining.
"If you see trees on lines or lines down, please stay well clear. Call us on 105 and we will send a team to make the site safe.
"We're hopefully coming to the tail end of the bad weather as we enter the evening and extra teams have been drafted in to continue repairs into the night as the weather subsides."
While many power cuts are restored within a few minutes by automatic technology, some of the damage requires difficult and complex repair work from teams of engineers on site. Some properties may be without power for longer depending on where the damage has taken place and how much damage has been caused.
Electricity North West offers extra support to customers who may find power cuts more difficult through its Extra Care Register. For more information and to register yourself or a friend or family member for free, visit www.enwl.co.uk/extracare.
You can prepare ahead of possible power cuts by charging phones and laptops, getting blankets and torches ready and speaking with neighbours or family members so you know what to do. For more tips and for live power cut information go to www.enwl.co.uk/powercuts.