Thirty Chatham homes were without power for almost 30 hours after supplies were cut on Wednesday.
Residents in Watson Avenue spent a night-and-a-half with no electricity because of an underground cable fault.
The outage happened at 9.50pm on Wednesday. Three homes are still without power today.
Engineers could not tackle the problem at night, so held back until 8.30am on Thursday to try and fix the problem.
The engineers were on site all day and managed to restore the power to the majority of home in the early hours.
One 73-year-old woman, said: “Most residents round here are pensioners and they’ll have felt the cold overnight.
“I’m lucky I keep candles and matches at home and a gas cooker and heater, but I’m sure a lot of my neighbours haven’t.”
Another woman, 80, who didn’t want to be named said: “It’s a right pain, It’s so cold outside, but I guess I am lucky as I have gas cooker, so at least I can have hot food and drinks."
An EDF Energy spokesman said: “Unfortunately it was not possible to restore power by re-routing supplies and, for reasons of public and staff safety, the decision was taken to send engineers out at first light the next day to locate the fault.
"Electricity was restored to all but the last three customers in Watson Avenue by 2.30am today
“Work will continue today to reconnect the remaining supplies as quickly as possible.
“We would like to apologise to all customers affected by this fault as we do appreciate how inconvenient it can be, particularly at this time of year.”