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
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.
Send your pictures to email@example.com, text them to 61124 or you have a large file you can upload here.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.