Four people are known to have have died in the storm 'St Jude' which brought heavy rainfall and winds of more than 112 km/h hit parts of the country.
Local authorities are clearing away the debris and fallen trees while engineers are working to restore power supply and railway service slowly to normal.
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Ferry crossings and several flights were also affected as the storm moved across the UK.
Tony Glover of the Energy Networks Association said that engineers had restored supplies to 100,000 homes overnight, but that 61,000 were still without power, most of them in eastern England.
At one point a total of more than 600,000 homes had lost their electricity supplies, the association said.
Winds of up to 99 mph were recorded at the Needles off the Isle of Wight, and up to 6cm of rain - half the monthly average - fell in a just few hours in areas including Hampshire and Devon, causing flash floods.
Rail services appeared to be running as usual in many areas this morning with South West Trains, one of the operators worst affected by the storm, saying it was running a normal service after nearly half of the 100-plus fallen trees that affected the UK rail network came down on the tracks it used.
Greater Anglia said it was still affected and that services would be cancelled or delayed.
In a statement on their website they said, "Despite working throughout the night on Monday Network Rail have found further trees on the lines and damage to overhead wires.
Ferry services from Dover are still understood to be delayed because of rough seas.
Dozens of areas in southern England still remain on flood alert, the Environment Agency said.
Insurers are still counting the cost of the storm, dubbed St Jude after the patron of lost causes on whose day it struck.
They said it was too early to tell whether it would compare with the multi billion-pound cost of previous severe weather events like the "Great Storm" of 1987.
Initial estimates of the level of financial damage are not expected until later this week, the Association of British Insurers said.
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