Areas affected include Brighton, Hampshire, Surrey and Oxfordshire.
In its warning, the weather service said the heavy rain is “likely to cause some disruption to travel” and that the flooding of a few homes and businesses is possible.
The Met Office said it expects 20mm-30mm (0.8in-1.2in) of rain to fall widely, with a few places seeing as much as 60mm (2.4in).
Although there is no warning in the capital, heavy rain is expected in the city overnight and throughout Monday.
After sub-zero temperatures over the weekend, it will feel slightly warmer with a high of 7C on Monday and 6C on Tuesday …