The River Ouse in York is among locations to have flooded in recent days
Dozens of flood warnings remain in place across Britain, with more heavy rain forecast for some areas later.
The Environment Agency still has a severe flood warning in place for the River Axe in Devon, meaning there is a danger to life.
There are 48 flood warnings and 133 alerts in England and Wales, and nine warnings and seven alerts in Scotland.
The weather could disrupt the day's two top sports events - Wimbledon and the F1 British Grand Prix at Silverstone.
A standard flood warning means immediate action is required, and a flood alert means people should be prepared for possible flooding.
'Surface water'
BBC weather forecaster Sarah Keith-Lucas said yet more unsettled weather was on the cards for Sunday and the week ahead.
She said: "There will be a much improved start to the day for south-west England although we will still have a lot of lying surface water following on from Saturday's wet weather.
"There will be sunshine and heavy showers through many parts of England and Wales but later on we will see that wet weather heading back in towards the north-east of England, so areas that have already seen torrential rain over the past few days will receive another dollop of rain."
She said there could be some thundery showers at Silverstone, and a showery day at Wimbledon.
There will also be a band of persistent rain across northern Scotland.
The Met Office has an amber weather warning for rain in Dorset until 06:00 BST.
It said the public should be prepared for the likelihood of surface water flooding and some disruption to travel and outdoor activities.
Silverstone 'challenge'
Rainfall totals on Saturday included 59mm (2.3in) on the Isle of Portland, 48mm (1.9in) at Exeter Airport, 43mm (1.7in) in Edinburgh and 37mm (1.5in) in Plymouth.
Officials at Silverstone, which is on the Northamptonshire/Buckinghamshire border, had to turn away thousands of fans wanting to see Saturday's qualifying sessions the amount of rain had left its car parks unusable.
All fans with tickets for Sunday's race have been advised they can attend, but told to allow plenty of time to arrive at the circuit. Up to 125,000 fans are expected for the race.
Managing director Richard Phillips said it would be "a bit of a challenge", adding "please bear with us, we are going to do our best".
In Northumberland on Saturday, a man in his 20s died when his car came off a road during torrential rain.
In separate incidents in Dorset, two people stranded on top of their car near the River Bride and a man stuck in his wheelchair in water at Burton Bradstock were rescued by coastguard teams.
8 July 2012 Last updated at 03:26 GMT
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