The Environment Agency said rainfall in Cumbria reached record levels with Seathwaite Farm recording 314.4mm (12.3 inches) in 24 hours.
During a 24-hour period Shap and Keswick in Cumbria recorded rainfall of 71.6mm (2.8in) and 64.2mm (2.5in) respectively.
The agency said the rainfall at Seathwaite Farm was a record for a 24-hour period in England, while the Met Office said the amount of rain expected in the west Cumbria area during the entire month of November had fallen in 24 hours.
Its Floodline service received more than 12,000 calls in 48 hours.
In Workington, Northside Bridge - the main bridge on the A597 into the town - collapsed, as did Lorton Bridge near Cockermouth and Southwaite footbridge in the town.
The prime minister said: "Everybody's thoughts and prayers are with those whose people who have suffered the impact of the most terrible floods in Cumbria and in other parts of England, Scotland and Wales.
"These last 36 hours have been particularly difficult for the people of Cockermouth and other people in the Cumbria area."
Downing Street said Environment Secretary Hilary Benn was in Cockermouth to meet the emergency services and assess what assistance was needed.
Drivers are being warned of "treacherous" conditions in much of Dumfries and Galloway and fire crews have been called to rescue a number of stranded motorists.
Up to 40 businesses were flooded in Dumfries and about a dozen roads in the surrounding area remain closed.
Business owners say it is the worst flooding they have seen in 20 to 30 years, and are calling for better flood defences in the Whitesands area of the town.
In north and mid-Wales, roads were closed and train services disrupted, and a brief power cut in Anglesey affected 2,000 homes.
The Environment Agency has in place four severe flood warnings - all in Cumbria - 15 flood warnings in the Midlands, Wales and north-east and north-west England and 31 less serious flood watches.
The Scottish Environment Protection Agency (Sepa) reported five flood warnings and 12 flood watches were in force, but there were no longer any severe flood warnings in Scotland.
The Environment Agency describes a severe flood warning as a threat of "extreme danger to life and property".
John Carlin, owner of the Allerdale Court Hotel in Cockermouth, said the amount of rainfall was "staggering".
"I have lived here for 15 years and have never seen anything like it," he said.
"It's desperate. The town centre is completely flooded, the only people out there at the moment are the emergency services. The water is up to the waists of the firefighters."
About 1,200 homes in the Cockermouth area and 349 around Keswick lost power on Thursday night, although United Utilities said later that services had been restored to 660 properties.
Some 20 schools in the area were earlier forced to close and several were turned into emergency shelters for more than 200 Cockermouth evacuees.
The flooding in Cumbria is the latest in a series of severe flooding events to hit the UK in recent years.
More than 1,000 houses and businesses in Carlisle, Cumbria, were overwhelmed by water in January 2005, when the city suffered its worst floods since the 1820s.
In June and July 2007 torrential rain lashed the country, flooding Yorkshire, Lincolnshire, Wales, the Midlands and the West Country. Among the worst-hit towns were Tewkesbury in Gloucestershire and Upton upon Severn in Worcestershire.
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