The Met Office had issued four yellow severe weather warnings for rain - and affected areas could see local flooding and disruption to transport.
An amber severe warning is in place for rain for London and the southeast until 11pm, meaning there is a risk of flooding and transport disruption with fast-flowing floodwater causing danger to life.
Wet and windy conditions are set to last well into the week, with cooler-than-average temperatures for this time of year.
According to the Met Office, Herstmonceux in East Sussex suffered some of the worst of the rain by 5pm on Monday, with 30mm.
However, total rainfall is predicted to be much higher after heavy thundery downpours in the evening.
"Homes and businesses are likely to be flooded, causing damage to some buildings," the Met Office said, adding 50mm to 60mm of rain could fall in four to six hours.
The average rainfall for the whole of June in the south east is around 50mm.
The Environment Agency (EA) has one flood alert on the River Ravensbourne in London covering the boroughs of Lewisham, Bromley, Greenwich and Croydon.
It said there was a risk of flooding for low-lying land, gardens and roads that are close to the river between 7am and 6pm.
The EA added: "We are actively monitoring the situation and are prepared to respond if required.
"Please avoid using low-lying footpaths near local watercourses and plan driving routes to avoid low-lying roads near rivers, which may be flooded."
Forecaster Simon Partridge said: "A number of spots around could see, within a few days really, a month's worth of rain, so a wet, windy, fairly cool week for most."
The first weather warning lasts until the end of the day, spanning from the Humber right down to the south coast, and from the East Midlands to Portsmouth.
The amber warning is in place all afternoon and evening.
Many places will see 20mm of rainfall, while isolated spots could see between 40mm and 60mm.
Weather warnings are in force for the whole of Tuesday up to midday on Thursday for northeastern England down to the Wash and as far west as the West Midlands.
In the South East, the top temperature is expected to be 14C or 15C (57F or 59F) - some 6C or 7C cooler than the average for this time of year.
The band of rain will head slightly north and west before settling.
Northern Ireland and Scotland will enjoy the best of the weather, staying mostly dry with sunny spells.
Areas under the rain band will experience temperatures ranging from 13C to 17C (55.4F to 62.6F).
On Wednesday and Thursday, eastern and northern England, 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".