Wales senior meteorologist Derek Brockway said a month’s rain fell in 24 hours at Swansea’s Victoria Park on Friday – which became the UK’s wettest place.
Some parts of south-east England also had more than half of their expected rainfall for the whole of September in 24 hours on Thursday and Friday.
Goudhurst in Kent and Farnham in Surrey saw 29.4mm (1.16 inches) and 28.4mm (1.12 inches) respectively.
Saturday’s yellow warning for rain covers all of southern and central England up to South Yorkshire, and all of Wales’ southern counties.
The Met Office said areas of heavy and thundery rain were expected to spread north, and then west, across England and Wales.
These areas of heavy rain may become more persistent across western areas during Sunday daytime, while slow-moving heavy showers and thunderstorms are likely to develop further east, the Met Office said.
There is a low chance that a few spots within the warning area could see 80 to100mm (3.1 inches to 3.9 inches) of rain by the end of Sunday.
These higher totals are slightly more probable in the southern half of the warning area.
