Initially in place from 1pm until 9pm today, the yellow warning has now been lengthened by two hours to run from midday until 10pm.
The area covered by the 10-hour weather warning has also been expanded, to now include parts of Staffordshire including Lichfield.
"Heavy showers and thunderstorms are expected to develop across central, southern and eastern parts of England on Wednesday afternoon," forecasters said.
"Whilst many places will only see relatively small amounts of rain, some slow-moving torrential downpours are possible. Where these occur, 20-30 mm is possible in an hour and in a few spots more than 50 mm could fall in three hours. Lightning will be an additional hazard, most likely over southern England."
The Met Office also warns of spray and sudden flooding that could lead to "difficult driving conditions and some road closures" and potential power cuts.
As well as Staffordshire, other parts of the West Midlands included in the warning include the eastern suburbs of Birmingham, Worcestershire and Warwickshire.
Meanwhile, the Environment Agency has issued a flood alert for the River Stour and Smestow Brook in the Black Country and South Staffordshire, and the Upper Tame.
The agency said: "This flood alert has been issued as heavy rain and thunderstorms have been forecast this afternoon. Significant impacts could be experienced from these thunderstorms. River levels are currently very low, but the heavy rain associated with these thunderstorms could lead to surface water flooding.
"There is, however, uncertainty, over the amount of rainfall expected and the exact location of these thunderstorms. We urge you to remain vigilant and avoid walking and driving through flood water."
The warning come off the back of a three-day heatwave that brought record-breaking temperatures to the UK, including the West Midlands.
Temperatures in the West Midlands peaked at 39C on Tuesday, while the first examples of temperatures in the country topping 40C were recorded, peaking at 40.3C in Coningsby, Lincolnshire.
Matthew Box, forecaster for the Met Office, said: "It's the warmest day on record across much of England and Wales. We also had records broken on Monday for Wales. It's been an amazing event."
West Midlands Fire Service said it had received 717 incident calls on Monday, 195 more than the previous day and 280 more than the number it received on Monday, July 11.
West Midlands Ambulance Service said it received 4,731 999 calls on Monday, lower than the 6,205 taken the previous Monday on July 11.