Thousands of customers were provided an "unacceptable service" following Storm Arwen, which caused nearly one million homes across the country to lose power.
Three network operators - Northern Powergrid, Scottish and Southern Electricity Networks and Electricity North West - have paid nearly £30 million in compensation to those affected by the bad weather last November.
Energy watchdog Ofgem has said that the trio have also agreed to pay another £10.3 million in " redress payments ".
Chief executive Jonathan Brearley said: "Distribution network companies faced challenging conditions in the aftermath of Storm Arwen and I pay tribute to the many colleagues in those companies who supported customers and worked to get them back on power as quickly as possible.
"However, it was unacceptable that nearly 4,000 homes in parts of England and Scotland were off power for over a week, often without accurate information as to when power would be restored.
"Network companies need to do better, not just to prevent power disruptions, but to ensure that when power is off, they work smarter to get people back on power quicker, and keep customers informed with accurate and timely information.
“This is the very least customers should be able to expect.
"The frequency of extreme weather events is only set to increase, so it is really important that industry, and those involved more widely, learn from Storm Arwen to better respond in future."
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