Further downpours on Christmas Eve may cause more flooding with the south-west badly hit, the BBC Weather Centre says.
Some rail services are still severely disrupted by the weather - with First Great Western advising people not to travel to south-west England.
With more rain expected, rivers in the South West will struggle to cope, the Environment Agency warns.
It says there is a heightened flood risk across Cornwall, Devon, Somerset, Dorset, Bristol, Hampshire, the Isle of Wight, West and East Sussex, North Yorkshire, south Wales, Ceredigion and Gwynedd.
Rail company First Great Western has advised customers with non-essential journeys in the South West not to attempt to travel on trains or replacement buses, because of flooding and poor road conditions.
Rail services continue to be suspended between Plymouth, Exeter St Davids and Taunton because of flooding. A plastic dam has been placed across the railway line at Exeter to minimise flood damage
Rail services in and out of south Wales have resumed, after being hit by "significant flooding"
Heavy rain has caused two landslides in Looe, Cornwall, which have cut off the nearby the village of Hannafore
Flood barriers have been put up in Stonehaven, Aberdeenshire, as water in the River Carron continues to rise
Further downpours on Christmas Eve may cause more flooding, with the South West badly hit, the BBC Weather Centre says.
BBC forecaster Holly Green said outbreaks of rain would be heaviest in Scotland on Sunday, with the rain returning to the south-west on Christmas Eve.
"Southern counties of England will also be plagued by some patchy rainfall [on Sunday], but elsewhere there is a bit of a respite from the wet weather.
"This rain will be falling on saturated surfaces and will continue to bring a risk of flooding."
She added that storm force winds for the Northern Isles and gales affecting Northern Ireland would transfer to parts of southern Scotland and northern England during Sunday morning.
'Flashy rivers'
'Flashy rivers'
Fire crews remained in the Cornish towns of Helston and Lostwithiel overnight to respond to any further flooding incidents.
Police have warned motorists not to use minor roads north of Barnstaple in north Devon, and tents have been issued to residents in Lostwithiel, Cornwall.
In Umberleigh, near Barnstaple, a woman was swept away from her car in the early hours of Sunday after flooding in the area.
A police helicopter found her clinging to branches of a tree on the banks of the swollen River Taw, Devon and Cornwall Police said.
Fire crews helped her to safety using a rigid inflatable, and she was treated for exposure to the water.
In the Cornish towns of Helston and Lostwithiel, fire crews remained overnight to respond to any further flooding incidents.
The River Cober, which broke its banks resulting in devastating flooding on Saturday, has started to recede. But the Environment Agency still has a severe flood warning in force in the Helston area.
The River Cober, which broke its banks resulting in devastating flooding on Saturday, has started to recede. But the Environment Agency still has a severe flood warning in force in the Helston area.
Nick Ely from the agency said: "There is nowhere in Cornwall that can really cope with the rain that's coming.
Nick Ely from the agency said: "There is nowhere in Cornwall that can really cope with the rain that's coming.
He went on: "Wherever the rain falls, the rivers will respond quickly. We have problems with 'flashy' rivers in Cornwall... where the rivers respond very rapidly with lots of run-off.
"Wherever the rain falls, the rivers will respond quickly. We have problems with 'flashy' rivers in Cornwall... where the rivers respond very rapidly with lots of run-off.
"We also have these problems with the catchments being so wet, that our bigger rivers... are also filling up and rising very rapidly".
"We also have these problems with the catchments being so wet, that our bigger rivers... are also filling up and rising very rapidly".
The Environment Agency has said there is a heightened flood risk across Cornwall, Devon, Somerset, Dorset, Bristol, Hampshire, the Isle of Wight, West and East Sussex, south Wales, Ceredigion, Gwynedd and North Yorkshire.
In Devon, residents in Pilton, near Barnstaple, may have to be evacuated if floodwater from the River Yeo reaches their homes. Emergency accommodation is being provided at Pilton Community College, police said.
BBC forecaster Holly Green said outbreaks of rain will be heaviest in Scotland on Sunday, with the rain returning to the south-west on Christmas Eve.
"Southern counties of England will also be plagued by some patchy rainfall [on Sunday], but elsewhere there is a bit of a respite from the wet weather.
"This rain will be falling on saturated surfaces and will continue to bring a risk of flooding."
She added that storm force winds for the Northern Isles and gales affecting Northern Ireland will transfer to parts of southern Scotland and northern England during Sunday morning.
South-west England is at further risk of some flooding issues and disruption when the rain is due to return on Monday, she added.
Emergency supplies
In Lostwithiel, Cornish disaster relief agency Shelterbox, which was recently delivering aid to Syria, is providing tents to residents who have been forced to leave their homes.
Joe Canon from the charity told the BBC they were also offering "good supplies of blankets, sleeping bags and general things that are needed".
Further west in Devon, police have warning the public not to travel on minor roads north of Barnstaple, which are closed due to extensive flooding.
Residents in nearby Pilton may have to be evacuated if floodwater from the River Yeo reaches their homes. Emergency accommodation is being provided at Pilton Community College, police said.
The River Caen in Braunton has also breached its banks for a second night, and police said the Braunton Academy has been opened as an evacuation assembly point.
The River Caen in Braunton has also breached its banks for a second night, and police said the Braunton Academy has been opened as an evacuation assembly point.
In other developments:
Rail company First Great Western has advised customers with non-essential journeys in the south-west not to attempt to travel on trains or replacement buses, due to flooding and poor road conditions.
Rail services continue to be suspended between Plymouth, Exeter St Davids and Taunton due to flooding. Trains are also not able to run between Bristol Temple Meads, Western-super-Mare and Taunton.
Heavy rain has caused two landslides in Looe, Cornwall which have cut off the nearby the village of Hannafore
Flood barriers have been put up in Stonehaven, Aberdeenshire, as water in the River Carron continues to rise
The Maritime and Coastguard Agency said its teams were distributing sandbags to protect properties and evacuate residents from houseboats at Velator Quay in Devon
In Exeter, resident Dan Regan told the BBC that flood barriers had been put up near his house.
"I've never seen them deployed here before and my neighbours, who have been here for 30 years, have never seen it either. I've never seen anything like the flooding we've had over the last month or so," he said.
A plastic dam has been placed across the railway line at Exeter to minimise flood damage. Steve Hawkins, from Network Rail, explained: "The last time it flooded we lost the railway for two or three days but we lost the signalling equipment, so we had restricted working, for two or three weeks.
"The idea of this is that we intend to try to protect the signalling equipment further down the track to make sure we can get the railway back up and working normally for our passengers sooner."
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