About 10,000 homes were left without power in South Wales and the West Midlands, as well as 2,000 in the South West, Western Power said.
This comes as South West England and Wales are being battered by winds of up to 71mph while the rest of the UK is experiencing powerful winds and more rain.
The outages were caused by weather-related problems, such as trees bringing down lines or debris hitting power lines a spokesperson said.
Waterlogged areas could be flooded as up to 40mm of rain is falling in some spots.
And the rain shows no sign of disappearing as the wet weather is set to continue into next week.
Shops have reported soaring sales of wellies and umbrellas in the face of the wet weather.
The Environment Agency has warned of the possibility of localised flooding across parts of the South West, South East and Midlands, East of England and Wales.
Tuesday will also see more heavy rain across Wales, the Midlands, the South East and East Anglia, but the rain will be more showery in the South West.
Many of the areas at risk of floods are in a state of drought at the moment, which is gripping the South East, East Anglia, the Midlands, the South West and south and east Yorkshire after two very dry winters in a row.
In its latest weekly drought briefing, the Environment Agency said all regions had now received above average rainfall for April, boosting river levels and providing relief for farmers, gardeners and wildlife in drought areas.
But groundwater levels remained low and the rain was not yet making a difference to the drought conditions, the agency warned.
And soil affected by prolonged dry weather is increasing the risk of flash floods as heavy rain quickly runs off hard, compacted ground.
Five flood warnings are in place for the North East, with properties at risk from rising water levels in a number of rivers including the Ouse in York. Householders are being urged to protect their homes.
The latest downpours come at the end of a particularly wet week for England and Wales, in which 42mm (1.7in) of rain fell in the South East and 55mm (2.2in) in the South West, which has now had 166 per cent of the average rainfall for April.
More than two dozen properties were flooded in St Helen Auckland, Co Durham, on Thursday, while there were localised floods in Devon and Cornwall earlier in the week.
Find out more about areas around the UK hit by harsh winds and heavy rain: