The alert is set to be in place on Monday, May 12 from noon until 10pm.
The Met Office said there could be up to 50mm of rain in just one to two hours.
This is expected to cause flooding and travel disruption.
People should also be aware of possible power cuts, and some buildings becoming damaged due to the weather.
The Met Office stated: “Thunderstorms developing across southern England on Monday afternoon and evening may cause disruption to travel and, in a few places, flooding.
“Thunderstorms and areas of rain are expected to develop over parts of southern England from early Monday afternoon.
“These may bring 20-25 mm of rain in an hour, and perhaps 40-50 mm in 2-3 hours in one or two places, leading to some surface water flooding, particularly if this falls over an urban area.
“The thunderstorms will clear from the west and northwest before midnight.”
London is expected to see highs of 23°C and lows of 15°C.
However, after the thunderstorms pass, Londoners can expect a week of warm weather.
On Tuesday, May 13, the Met Office predicts temperatures of 24°C, which will be the highest in the capital this week.
The weather is expected to remain sunny throughout the week, with temperatures ranging from 19°C to 23°C.
The outlook for the UK generally is that the south will experience the warmest weather, while the north will see more unsettled weather, with a mixture of sun and showers.
For the latest updates, people can visit the Met Office website, or download the Met Office app.
