Police Constable Bill Barker, 45, was thought to have been swept away after a bridge collapsed in Workington in the Lake District, where floodwaters reached "biblical" proportions, according to a local lawmaker.
"I'm very sad to have to report we've recovered a body on the beach of an individual. That has not been identified. Our thoughts go out to Pc. Barker and his family," said Cumbria Assistant Chief Constable Jerry Graham.
More than 200 people were forced to leave their homes in nearby Cockermouth overnight, four bridges collapsed into raging rivers and main roads were blocked.
In Cockermouth, helicopters winched people to safety and rescue boats negotiated streets turned into canals after rivers burst their banks.
Lifeboat service the RNLI, which also helped search for the body, said conditions were atrocious.
"There is a massive current coming down through the Derwent (river) so, although the sea isn't very rough, conditions for the RNLI volunteers searching in the river basin have been very challenging," said RNLI manager Brian Ashbridge.
"It's absolutely horrendous. There is a huge amount of debris around in the water at the moment as well, which adds to the difficulties," he added.
Tony Cunningham, the Member of Parliament (MP) for Workington, told Sky News television that the flood was "of biblical proportions" and seen "once every 1,000 years".
"The force of the river was absolutely incredible. This is a stone bridge, to wash away a bridge of that size and dimension is incredible," he said.
Prime Minister Gordon Brown pledged support, saying he had spoken to Environment Secretary Hilary Benn and told him "that if there are facilities needed we will make them available."
Floods also hit neighbouring Ireland, where troops were sent to assist emergency services in six cities and towns in the south and west of the country after days of sustained rainfall.
A number of rivers burst their banks, roads were closed and trains cancelled in the worst-hit areas. A coastguard helicopter rescued a family including an 87-year-old woman as their home was surrounded by rising floodwaters.