The warnings, which indicate a possible danger to life, have been issued around the towns of Egremont and Kendal.
The north of England and parts of Wales are warned to prepare for the risk of flooding, as heavy rain approaches.
There are amber warnings, meaning "be prepared", for Greater Manchester, and North and West Yorkshire.
People in certain locations around Kendal and Egremont, on opposite sides of the Lake District, have been advised to move out to stay with family and friends who live in areas with lower risk of flooding.
Reception centres have opened at Kendal Town Hall and West Lakes Academy.
South Lakeland District Council said up to 1,000 properties could be at risk and that military personnel could be deployed to install temporary flood defences to protect vital infrastructure.
The worst of the weather is expected from Saturday evening through to Sunday.
In some places, a month's worth of rain has been forecast to fall in 24 hours.
Falling on already saturated ground, it is likely to cause localised surface water flooding and high river levels, the Environment Agency said.
The Met Office has also warned of possible flooding in parts of Scotland in the wake of Storm Abigail.
Nicola Willis, from the Met Office, said high ground was likely to be most affected by heavy rain.
"These areas have had a lot of rain already this week and they are already quite saturated," she said.
"We are expecting the rain to be heavy and persistent, although the heaviest rain will not necessarily continue through the whole of the warning period."
Cumbria was hit by severe floods in November 2009.
During those incidents, Pc Bill Barker, 44, died after the bridge he was standing on collapsed in Workington, a town about 13 miles north of Egremont.
Craig Woolhouse, from the Environment Agency, said it was working closely with emergency services to prepare for any problems.
He added: "Our teams are already in action clearing watercourses, maintaining existing defences and standing ready to deploy temporary pumps and defences where these can be effective."
The latest band of rain comes in the wake of Storm Abigail, which closed schools and brought down power lines in parts of Scotland.
The Christmas lights switch-on in Bradford on Saturday was cancelled because of the weather forecast.

George Rogerson, 22, of Plean, admitted stabbing Leon Cairney 11 times in the village last December after the pair rowed in the street in the early hours.
He told the High Court in Dundee he had been provoked into the attack on the 25-year-old.
Judge Lord Kinclaven deferred sentence until November 20 and Rogerson was remanded in custody.
Rogerson had earlier tried to plead guilty to the lesser crime of culpable homicide, a plea rejected by the Crown.
He then went on trial accused of murder at the High Court in Dundee - a charge he denied.
The jury was told how Rogerson had rowed with neighbour Simon Blair, who had then called on Mr Cairney to help confront Rogerson.
Giving evidence in his own defence, Rogerson said he had grabbed a kitchen knife from a block and stormed out the back door during the incident.
He said: "I went out to the side of the house - I opened the side gate and when I did that they came flying in.
"It was Leon Cairney and Simon Blair - I recognised them both.
"I had the knife in my right hand. We started fighting and he was hitting me on the side of the head and I started stabbing him.
"It stopped when he let me go and fell backwards."
The court earlier heard from a pathologist that Mr Cairney had been stabbed 11 times - including four in the chest and one in the abdomen that had penetrated up to the hilt of the knife.
Rogerson said he had "panicked" by going outside with the knife.
A jury of eight men and seven women took two hours and 50 minutes to find him guilty of culpable homicide.

The Highlanders, relegated from the top flight last season, have appointed John Robertson as Richie Foran's successor.
Elsewhere, Dumbarton host Morton, St Mirren face Falkirk, Queen of the South take on Brechin City.
Newly-promoted Livingston welcome Dunfermline Athletic for their first game of the season.
Twelve severe flood warnings have been issued for Cumbria and Lancashire, warning people to take immediate action and prepare for flooding.
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A man who stabbed a former soldier to death in Stirlingshire has been convicted of culpable homicide.
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Inverness CT will open their Scottish Championship campaign at home to Dundee United when the 2017-18 gets under way on 5 August.