Emergency teams are on standby in flood-hit areas of the UK in case further downpours add to the problems.
Flooding is still affecting villages such as Toll Bar, near Doncaster
Forecasters said up to 20mm (0.8in) of rain could fall in parts of England and Wales, with possible localised floods.
Troops have joined fire and lifeboat crews in South Yorkshire, where some areas remain badly affected by floods.
The Environment Agency said the general situation had eased overnight, and rain is expected to be lighter than earlier this week when four people died.
The agency said the heaviest rains had fallen outside the flooded areas over the last few days and the situation across the Midlands had greatly improved with river levels starting to fall.
There are four severe flood warnings in place - three on the River Don and one on Ea Beck.
The agency's head of flood policy, Philip Rothwell, said: "The picture at the moment is of heavy showers coming through, and coming through quite quickly rather than the sort of persistent rain sitting there for hour after hour, which is good news I think."
The Met Office has in place early severe weather warnings of heavy rain for the whole of England and Wales until Tuesday.
Heavy showers are expected during Sunday and Monday, with the possibility of more prolonged rain during Tuesday.
BBC weather forecaster Penny Tranter said: "Overnight rain has moved away and we're left with some fairly swift-moving heavy showers across England and Wales.
"In terms of heavy rain, it will not be as bad as it has been. There's a risk of localised flooding."
Up to 25mm (1in) of rain fell on Saturday.
Rest centres have been made ready and at-risk areas have been sand-bagged. Residents in some areas have been urged to pack emergency bags in case of evacuation.
A national flood support centre has been set up in Worcester to respond to further outbreaks of severe weather.
The worst-hit areas are at Bentley and Toll Bar near Doncaster, where giant pumps are being used to carry water from the deluged village via hosepipe to the River Don two miles away.
Doncaster North MP Ed Miliband said he was looking into how he could help his constituents.
"This is no normal situation, this is a real, very, very bad serious emergency situation.
"That's why we've got the pumping equipment in, and it's why also I am talking to government colleagues about what more can be done to help people financially and in other ways to help them out of their situation."
Further developments include:
- Electricity has been restored to more than 80,000 homes affected by rains and flooding in South Yorkshire, but 400 homes still have no power
- West Yorkshire Police said four people were arrested on Saturday for theft from flooded properties in Wakefield and that officers were patrolling the area
- More than 350 people were evacuated from their homes in north Doncaster after the river burst its banks, and firefighters are pumping water out of the area
- The Association of British Insurers (ABI) said so far 27,000 homes and 5,000 businesses had been affected across the country and that clean-up costs could reach £1bn
Two people died in Sheffield, including a teenage boy, a man died in Hull and a driver died in Worcestershire during the flooding earlier in the week.