Storm Babet: Fresh weather warnings for Leeds, Sheffield, York, Rotherham, Hull, Whitby and Scarborough as heavy rain set to continue
The Met Office issued the yellow warning for "heavy rain" which could lead to further flooding in the East Midlands, including Nottinghamshire and Lincolnshire, as well as much of Yorkshire, including Sheffield, Leeds and York, and Humberside.
An estimated 30,000 properties have needed protection against rising water levels, the EA said.
A total of 13 areas broke their daily rainfall records for October last week, including sites in Suffolk, South Yorkshire, Lincolnshire, Wiltshire, Kincardineshire, North Yorkshire, Nottinghamshire, Northumberland, Derbyshire and Humberside, the Met Office said.
Anna Calder, spokeswoman for the EA, said significant river flooding impacts will continue for parts of the Midlands until Friday, with minor impacts continuing in parts of the Midlands and the north-east of England until Wednesday.
Significant river flooding is also possible but not expected in parts of England on Tuesday and Wednesday, with minor impacts possible more widely, due to further heavy rainfall falling on sensitive catchments.
The Met Office warning, which is in place for between 3am and 4pm on Tuesday, stated: "There is a small chance that homes and businesses could be flooded, causing damage to some buildings. There is a small chance of fast-flowing or deep floodwater causing danger to life. There is a small chance that some communities will become cut off by flooded roads."
The latest warning comes after 83-year-old Maureen Gilbert was found dead in her flooded home in Tapton Terrace, Chesterfield, Derbyshire, on Saturday morning.
Mrs Gilbert's neighbours said 5ft of water had engulfed the inside of their properties "within minutes" of the River Rother bursting its banks.
Asked if flood defences were adequate, Ms Calder said the EA has been "working around the clock with its partners to help reduce this risk".
She added: "We've put barriers up to help protect communities as well as employing pumps in key locations."
Derby City Council said record-breaking water levels had been seen in the River Derwent and warned cleaning up after the floods could take several days.
A 56-year-old driver died when a tree fell on his van near Forfar in Angus on Thursday while a man in his 60s died after getting caught in fast-flowing floodwater in the town of Cleobury Mortimer, Shropshire, on Friday.
Unsettled weather will continue this week but it will be "nowhere near as impactful as last week", Nicky Maxey, spokesperson for the Met Office said.
She said: "On Monday northern areas will be mostly dry with sunny spells, there will be showers in the South West and Northern Ireland, and heavy rain on the Isles of Scilly."
Tuesday will be mainly dry but there will be outbreaks of rain which will push northwards through the day, although the North West will probably stay dry, the forecaster added.