The warning, issued at 10.46am this morning, is valid between midday and 9pm on Saturday, July 31 – with thunderstorms potentially causing disruption to travel.
There is a "good chance" driving conditions will be affected by standing water and possibly hail, leading to longer journey times by car and bus, say forecasters.
Delays to train services are possible. And flooding of a few homes and businesses is possible.
Some short term loss of power is possible, as is damage to a few buildings or structures from lightning strikes.
A Met Office spokesman said: "Although many places will miss them, heavy showers and some thunderstorms are expected to develop this afternoon over some southern and eastern parts of England.
"Downpours could bring around 20 mm of rain within an hour, and perhaps 30-40 mm in a few hours for a few locations, leading to possible surface water flooding in places.
"Lightning and hail are most likely to occur across southeastern counties of England. The showers and thunderstorms will ease by late evening."