The BBC is not responsible for the content of external internet sites
RNLI lifeboat operations manager Captain Brian Ashbridge said there was a "massive current" travelling down the Derwent, making conditions for the searchers "very challenging".
Police in Cumbria have received a high volume of calls about missing people and more than 1,200 people were left without electricity overnight.
In Cockermouth centre, water levels had reached more than 2.5m (8ft 2in) and the Armed forces were also drafted in to help with the rescue operation.
This included three RAF search and rescue helicopters from bases at Valley, Leconfield and Boulmer and two RAF mountain rescue teams.
Five RAF Sea King helicopters were sent to the Cockermouth area, along with RNLI lifeboats and coastguard teams.
Andy Clift, the RNLI's divisional inspector for the north, said the service had rescued dozens of people in dangerous conditions.
He said: "We've experienced very strong river flows, over 20 knots, which make operating boats in those conditions quite hazardous.
"Certainly earlier on, when the flood water was at its peak, we were getting a lot of debris, including cars, being swept down the river and that also was very hazardous in the darkness, for our crews."
The Environment Agency said rainfall in Cumbria reached record levels with Seawaite Farm recording 314.4mm (12.3 inches) in 24 hours.
Pc Bill Barker is a father of four with 25 years service
Environment Agency chairman Chris Smith described the rainfall as "unprecedented".
The agency said the rainfall at Seawaite 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.
Prime Minister Gordon Brown 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.
"All the emergency services are doing everything they can to help people who are in difficulty as a result of the floods.
"It has been the worst rainfall according to records that we've seen in Britain at any time since records began and 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.
Mr Benn earlier told the BBC: "We have seen extraordinary amounts of rainfall. We've seen the impact of that with the terrible flooding which has affected people."
This is an extremely serious incident - our thoughts are with those people whose homes have been flooded
Flooding was also reported in Dumfries and Galloway in Scotland, where 30 roads closed in "treacherous" conditions.
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 - 23 flood warnings in the Midlands, Wales and north-east and north-west England and 51 less serious flood watches.
The Scottish Environment Protection Agency (Sepa) reported six severe flood warnings, 10 flood warnings and 15 flood watches in force.
RAF Squadron Leader Dave Webster 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.
ON THE SCENE - 0500 GMT
The BBC's Laura Bicker, in Cockermouth
Cockermouth High Street looks more like a rapidly flowing river at the moment.
Shops that had just done up their fronts for Christmas are now only accessible by boat.
The RNLI, the fire service, mountain rescue and the police are all here working together to try to evacuate people from their houses.
Overhead, there's a helicopter from the RAF taking people off the roofs of their houses and from windows.
It looks very much like a disaster zone and it's feared that the river levels are still due to rise further.
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.
Some 20 schools in the area were earlier forced to close and several were turned into emergency shelters for more than 200 Cockermouth evacuees.
Environment Agency chairman Lord Smith said: "This is an extremely serious incident - our thoughts are with those people whose homes have been flooded."
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".
Sepa has six severe flood warnings in place in Scotland, covering three sections of the River Tweed, the River Earn, Yarrow Water and the River Isla in Perthshire.
A landslip between Carlisle and Penrith caused the West Coast Main Line from London to Glasgow to close - but it has since re-opened.
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.
High winds
The AA said it was "flat out" rescuing stricken cars and advised against all but essential travel.
Richard Westmoreland, the motoring organisation's water rescue technician, said: "Conditions in Cumbria have been horrendous - the worst I've seen."
During a 24-hour period Shap and Keswick in Cumbria recorded rainfall of 71.6mm (2.8in) and 64.2mm (2.5in) respectively.
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.
Are you in one of the areas on flood alert? What are conditions like where you are? Send us your comments and pictures.
One-Minute World News 
E-mail this to a friend 
Printable version 
This is an extremely serious incident - our thoughts are with those people whose homes have been flooded
BBC News
Bookmark with:
What are these?