He said: "Our thoughts are with all those who have been impacted by these floods and our thanks go out to the emergency services who continue in their extraordinary efforts to help the people affected."
Environment Secretary Hilary Benn, who is travelling to Cockermouth, said the situation was "very serious".
He told BBC Breakfast: "We have seen extraordinary amounts of rainfall. The rain gauge at Seathwaite registered 314mm [12.4in] in 24 hours which could make it the wettest day ever recorded, and we've seen the impact of that with the terrible flooding which has affected people."
The Environment Agency has in place four severe flood warnings - all in Cumbria - 28 flood warnings in the Midlands, Wales and north-east and north-west England and 63 less serious flood watches.
In Scotland there are nine severe flood warnings, 10 flood warnings and 14 flood watches in force.
In Cumbria, the main bridge into Workington on the A597 collapsed along with Lorton Bridge near Cockermouth and Southwaite footbridge in the town.
Five RAF Sea King helicopters were sent to the Cockermouth area, along with RNLI lifeboats and coastguard teams, to help with the rescue effort.
The RAF said conditions were "atrocious", with water levels in some parts of the town reaching about 8ft (almost 2.5m).
"The situation has continued to deteriorate over the past two hours with people being forced to break through the rooftops of houses as they frantically seek escape from rising floodwaters," it said in a statement.
Wing Commander Peter Lloyd said: "We are concentrating on getting people away from imminent danger and delivering them to what is comparative safety."
RAF Squadron Leader Dave Webster later said more than 50 people had been rescued by helicopter, while about 150 more had been helped to safety by the RNLI and other emergency crews.
"There have been no serious injuries as a result of the floods, just a few people treated at the scene for minor bumps and scrapes," he added.
Earlier, Ch Supt Steve Johnson said flood defences installed in Carlisle following the 2005 floods appeared to have worked, but added: "We are not taking anything for granted."
John Carlin, owner of the Allerdale Court Hotel, 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.
Lifeboats have been rescuing people from their homes in Cockermouth
The Ministry of Defence said the Army had been drafted in to help with door-to-door work in Cumbria.
Some 20 schools in the area were earlier forced to close and several were turned into emergency shelters for more than 200 Cockermouth evacuees.
Robert Runcie, the Environment Agency's director of flood and coastal risk management, said at least 500 homes could be flooded in and around Cockermouth.
There are currently four severe flood warnings in Cumbria, in Cockermouth, Keswick, Southwaite Bridge and Eamont Bridge.
The Environment Agency describes a severe flood warning as a threat of "extreme danger to life and property".
There are nine severe flood warnings in place in Scotland, covering three sections of the River Tweed, two sections of the River Earn, Yarrow Water, Teviot Water, the River Isla in Perthshire and the River Teith at Callander.
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