Severe yellow weather warnings have been issued by the Met Office across the most of England and parts of Scotland.
Weather forecasters have said storms will increase the chance of flooding, which could cause possible travel disruption on Tuesday.
There is also the chance there could be some hail in northern parts of England.
The Met Office said: "Heavy showers and thunderstorms will continue to spread north-east across England and Wales, while also increasing in frequency during the day.
“In a few places there is the potential for 20mm (0.8in) to 30mm (1.2in) of rain to fall in an hour and 30mm (1.2in) to 50mm (2in) of rain to fall in three hours.
“Hail is also possible, mainly over northern England.”
The South East and East Anglia have not been covered by the weather warning, which runs until the end of Tuesday.
The area covered by a weather warning for Wednesday includes parts of Scotland, North Wales, north England and the Midlands.