The south west of England, already on the receiving end of a winter battering, was worst affected with 14,000 properties left without power, according to Western Power Distribution
The company said "airborne debris" carried by 120-130 kph winds had damaged overhead lines.
"We will be working into the early hours to restore power providing it's safe to do so," said a spokesman.
Heir to the throne Prince Charles earlier met residents, farmers and emergency staff in the stricken county of Somerset, in southwest England.
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His visit comes as the government of Prime Minister David Cameron faces anger over its response to the floods.
Charles, 65, received a round of applause from locals as he arrived in the town of Stoke St Gregory.
The Prince of Wales was later due to travel by boat to the village of Muchelney, which has been marooned by floodwaters for more than a month.
"Prince Charles can't change anything, but people are pleased that he's coming," said Catherine Denny, a retired school teacher.
"The band of rain which is moving across from the south west will continue its journey north-eastwards during the course of the night, with fragmented outbreaks of rain -- still pretty heavy -- following on behind," said the Met Office.
"It will continue to be very windy. We can expect to see gusts of 60-70mph quite widely across parts of south Wales, Devon and Cornwall, Somerset and Dorset"
The Environment Agency issued four severe flood warnings for the region, indicating that the conditions posed a danger to life.
Cameron's government has come under fire after an official warned Monday that Britain may have to choose between protecting its towns or its countryside from flooding in the future.