The Met Office issued a 'danger to life' amber weather warning as a month's worth of rain fell in one day in some parts of the country.
Kent Police urged people to avoid travelling unless absolutely necessary due to severe flooding.
The force closed the M25 between junctions five and four when they discovered sinkholes in the central reservation of the motorway following a crash.
Pictures have been shared on social media showing vehicles trapped in floodwater in London and south-east England, with some roads being completely cut off.
The Met Office issued an amber weather alert for London and south-east England yesterday, warning that fast-flowing water could put lives at risk.
It is predicted the weather will likely cause delays for commuters and power cuts at homes and businesses this week.
Yesterday, rail lines were affected by the downpours, with Regent's Park tube station in London shut due to flooding.
A lorry also flipped onto its side in wet conditions on the M25, between junctions eight and seven, yesterday.
Forecasters now believe some parts of the UK could be inundated with more than 100mm of rain this week.
According to the Met Office, Herstmonceux in East Sussex had had the worst of the rain by 5pm yesterday, with 30mm.
Between 50mm and 60mm was expected over four to six hours in London and south-eastern counties until about 11pm.
The average rainfall for the whole of June in the South East is around 50mm, the Met Office said.
On Tuesday, yellow warnings are in place for Exmoor and a large area of eastern and north-eastern England, where rainfall could reach 60mm.
On Wednesday and Thursday, similar areas, plus northern Wales, could be struck by 60mm to 80mm of rain, and possibly even up to 100mm.
Met Office meteorologist Alex Burkill described the figures as the "worst-case scenarios" but added that people need "to be aware that we're in for some treacherous weather".
"If you add it all up some places are likely to see over 100mm this week, which is around double the average they would get in the whole of June," he said.
The Environment Agency has issued a flood warning covering the River Wandle at Morden in south London, urging people to take immediate action as the flooding of properties is expected.
The agency said on its website shortly before 6pm on Monday: "River levels have risen as a result of localised thunderstorms. Flooding of property is expected imminently.
"Please take action. Further thunderstorms are forecast over the next six hours.
"We expect river levels to remain high until around 10pm on Monday evening."
Residents are being told to avoid low-lying footpaths near local watercourses and plan driving routes to avoid low-lying roads near rivers which may be flooded.
A further six flood alerts are warning people to prepare for potential flooding in parts of south London, Nottinghamshire, Wiltshire and Devon.
