The downpour is "loosely" linked to Hurricane Humberto, which hit the edge of Bermuda and is travelling across the Atlantic towards Britain.
It was a category three storm at its peak on Wednesday and Thursday.
The Met Office has issued the yellow weather warning for rain for Tuesday, for an area which stretches from London and the South East to the South West, southern Wales and Herefordshire.
It is set to last throughout Tuesday until 3pm.
Met Office meterologist Luke Miall said: “We could see 20mm to 40 mm of rain within nine hours and possibly the worst case scenario is of 70mm in some spots.”
He said "there is the possibility of the odd rumble of thunder" in some areas on Tuesday in contrast to recent dry days and sunshine.
Travellers, particularly on Tuesday morning, should brace themselves for disruption.
Bus and train journeys could take longer, there could be flooding on roads, and homes and businesses could also be drenched in the downpour.
The weather warning states: "Spells of rain and heavy showers are expected to affect southern parts of England and Wales during Tuesday."
It continues: "The heaviest rainfall is likely to be during the morning.
"Around 20 mm to 40 mm of rain is expected to fall quite widely, with the potential for up to 70 mm in a few locations.
"Much of the rain will fall in a relatively short space of time, typically less than six hours.
"The location of the very heaviest rainfall is currently still somewhat uncertain."
Mr Miall said there will still be a wet start to the week on Monday, but that any pockets of sunshine over the following days could see temperatures in the low 20s which is slightly warmer than normal for the time of year.