The warning is in place between 6am and 11.59pm on Saturday.
A spokesperson for the Met Office said: "An area of heavy rain and some thunderstorms is expected to develop on Saturday morning over southern England and then move northeastwards before clearing into the North Sea Saturday afternoon.
"Many places will see a short period of heavy rain whilst some may see a more prolonged period of rain along with some intense bursts, with lightning and hail.
"Under the heavier rain some sites could see 30-40 mm rain falling in a few hours.
"Once this clears, further heavy showers are expected to break out. These will be more hit-and-miss with many sites staying dry following early rain, but where they do occur, there is a chance of 30-35 mm rain falling in an hour, again accompanied by lightning and hail."
Heavy rain and thunderstorms may bring some disruption on Saturday. What could we see:
There is a small chance that homes and businesses could be flooded quickly, with damage to some buildings from floodwater, lightning strikes or hail
Where flooding or lightning strikes occur, there is a chance of delays and some cancellations to train and bus services
Spray and sudden flooding could lead to difficult driving conditions and some road closures
There is a small chance that some communities become cut off by flooded roads
There is a slight chance that power cuts could occur and other services to some homes and businesses could be lost