They have, however, warned that disruption is likely to occur to those travelling and also to businesses.
The areas set to be affected are located in London and the South East of England, the South West of England and Wales.
Potentially dangerous weather conditions are forecasted to begin at 2pm tomorrow.
The Met Office said that “rain, heavy at times, is likely to cause some disruption on Saturday afternoon and night”.
Commenting, the Met Office said: “Rain will turn persistent and heavy at times across the warning area through Saturday afternoon and evening.
“Accumulations of 20 to 30 mm are expected with 45 mm possible on high ground.
“Given existing saturated ground there is a risk of some localised flooding.”
There are currently no weather warnings in place from the Met Office covering next week.