The yellow warning covers much of the country, including Shropshire and Powys, and runs from 10am until 11.59pm.
The sudden change in weather is expected to cause travel disruption and flooding in a few places.
In its warning, the Met Office said: "Thunderstorms are likely to break out in some areas, particularly during the afternoon and early evening. While most places will probably miss them, where thunderstorms do occur there is a chance that in a few places up to 40 mm of rain could fall in an hour or so and 40 to 60 mm could fall in two or three hours.
"These torrential downpours may be accompanied by frequent lightning, whilst gusty winds and hail may also affect a few places. The exact location of the thunderstorms will be hard to pinpoint, so the warning area will be kept under review and updated if necessary."
The Met Office also warns there is a "small chance that homes and businesses could be flooded quickly, with damage to some buildings from floodwater, lightning strikes, hail or strong winds".
With the roads already busier than normal due to rail strikes, drivers have been warned to expect further delays and disruption to their travel due to more difficult driving conditions caused by spray and sudden flooding, which could also lead to some road closures.
They also warning of a small chance of fast flowing or deep floodwater causing danger to life and some communities being cut off by flooded roads, as well as a "slight chance that power cuts could occur and other services to some homes and businesses could be lost".
The Met Office's warning comes as Shropshire and Mid Wales enjoyed clear blue skies and temperatures of around 25C.
Thursday's weather warning covers much of England and parts of Wales, reaching Cheshire in the North West, the whole of East Anglia, all of the South and South East of England, and stretching to Somerset and Cardiff in the West.