It comes as another storm of heavy rain and strong winds arrives in the UK, bringing with it a risk of flooding and disruption.
Tens of thousands of homes across the south east of England, north Wales and Cumbria have been without electricity over the last week because of damage caused by the storms.
The ENA tweeted last night: "Engineers have this evening reconnected those who lost power due to the severe weather damage."
Forecasters have said the latest storm pushing in from the Atlantic will cross the UK from west to east today.
The Met Office has issued a severe weather warning over fears of strong gales of up to 80mph affecting Wales, southern, western and northern England and Scotland. It has also warned of the danger of ice patches in the south west tonight as temperatures drop to below freezing.
George Goodfellow, a forecaster for MeteoGroup, said: "Normally, we would say this is a typical winter storm but because we're still recovering from a string of other storms it is likely to cause more disruption and flooding." He said the south west will continue to bear the brunt of the storm.
Some 1,300 properties have been flooded during the recent storms in England, the EA said. Meanwhile energy companies have been criticised for their slow reaction to storm damage.
The executive of one of the UK's biggest power distributors has admitted its efforts to restore power to thousands of people should have been better.
Basil Scarsella, chief executive of the UK Power Networks, told The Mail on Sunday it was not prepared for the storm and too many staff were on holiday.
The company, which owns electricity lines and cables in London, the south east and east of England, said it will increase payments for 48 to 60-hour outages from £27 to £75 for those affected on Christmas Day as "a gesture of goodwill".
Additional payments will be made to customers who have been without electricity for longer than that time - up to a maximum of £432. Mr Scarsella said: "We could not have avoided the damage caused by the storm but we could have responded to it better.
"A lot of our employees had gone away for holidays so it meant we had a level of depletion in our resources - and that caused problems with getting people's power restored.
"It's difficult to justify saying the company has performed well when customers have been without power for five days, but once we had an idea of how bad it was we were able to mobilise as many engineers and office staff as possible."