Workington and Penrith had been hit particularly badly by the storm, the company added.
Alan Astall, from Electricity North West, said: “The network has held up well and our automatic restoration systems have kicked in in many areas, rerouting power to customers while engineers carry out repairs.
“Our teams are working hard to restore the remaining properties today, while continuing to monitor the weather.”
Homes in south and west Wales, along with the east of England and West Midlands, have also been left without power after Storm Bert brought snow, high winds and heavy rain to the UK.
Energy Networks Association (ENA), which represents UK energy networks, has said its members have engineers on standby as the worst of the weather was “yet to arrive”.