Engineers have been working to restore power but more than 7,000 homes are still without electricity.
In Dawlish, Devon, a section of sea wall under the railway line collapsed, leaving the track suspended in mid-air.
UK’s Prime Minister David Cameron will chair a meeting of the Cobra emergency committee later to consider the government’s response.
It is the first time this year that the prime minister will have chaired a meeting of Cobra to discuss the floods and follows widespread criticism of Environment Secretary Owen Paterson’s handling of the crisis.
The prime minister’s office said David Cameron was anxious to ensure that “all that can be done is being done”.
Earlier, First Great Western said all lines between Exeter St Davids and Penzance were closed because of adverse weather conditions and it advised against travel for the rest of the day.
Part of the sea wall at Dawlish, which is between Exeter and Cornwall, has collapsed and the railway station and tracks have been severely damaged by huge waves, driven by gale-force winds.
Western Power Distribution said about 44,000 customers had been affected by power cuts since Tuesday afternoon and 7,400 homes in south-west England remained without power.
The Met Office said gusts of up to 70mph and 20mm of rain had spread from the South West to south-west Wales and eastern Northern Ireland overnight.
Western Power Distribution said there had been high voltage faults due to debris being blown around in Devon and Cornwall.
Teams of engineers worked through the night to try to fix the faults, and the company said it would also switch circuits to work around individual faults.
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