Power has been restored to all but 2,525 properties in Lancaster, and a further 1,514 remain without power in Cumbria due to the flooding.
A statement this morning says: "Teams from the network are continuing to work around the clock and began gradually restoring power from 06.30 following through-the-night repairs to the main substation in the area.
"All customers that we can restore from the substation should be back on by late this evening, however some issues may remain with local flooding for a few customers."
Mark Williamson, operations director for Electricity North West, said: "This is an incredibly difficult time for everyone involved and we are doing absolutely everything we can to provide power to everyone affected by this incident.
"Thank you to everyone for the goodwill shown towards our engineers who are putting in a monumental effort working in shifts 24 hours a day to get the job done."
"Teams from Electricity North West are also working in Cumbria to restore power to the remaining 1,514 properties affected in the county after flooding cut power to a number of local substations.
"Electricity North West have sent catering vans to eight locations across Carlisle and Lancaster to provide hot food and drinks to customers.
"We are continuing to proactively contact vulnerable customers and provide additional support to them where we can."
Vulnerable customers, including some older or disabled people, or those with a medical dependency on electricity, can also sign up to the Priority Services Register here or contact Electricity North West on 0800 195 4141.