Alerts have been issued for the Midlands, the South West, North West, South East, London, East Midlands and the West Midlands.
Thunderstorms are likely to occur in these areas, according to the Met Office.
The forecaster says driving conditions “are likely to be affected”.
Meanwhile, “some flooding of a few homes and business” is “likely”, it warns.
Buildings may also be damaged by lightning strikes.
Delays to train services are also described as “likely”, as is short-term loss of power in areas.
The Met Office warned: “Thunderstorms are likely to develop across parts of southwest England and Wales during Monday afternoon and become more organised through the evening.
“Lines of thunderstorms are expected to then move north during the early hours of Tuesday and gradually weaken as they clear into northern England before dawn.
“Whilst some places will see little or no rainfall, a few locations may see torrential rain with 20-30 mm falling in one hour and 50-80 mm in 3 hours.
“Additional hazards accompanying stronger thunderstorms include frequent lightning, hail and gusty winds, particularly during the evening period.”
The lightning caused by these storms could lead to power surges.
Residents are advised to unplug any non-essential appliances if they are not using a surge protector to mitigate the effects of this.
If you are caught in a storm, seek shelter.
Hearing thunder means you are already within range of where the next ground flash may occur, according to the Met Office.
Lightning can strike as far as 10 miles away from the centre of a storm.
Driving conditions are predicted to be affected by spray, standing water as well as hail.
This will lead to longer journey times by car and bus.
For those planning to drive, the Met Office states: “Even moderate rain can reduce your ability to see and be seen.
“A good rule of thumb is ‘if it’s time for your wipers, it’s time to slow down’.
“If heavy downpours are expected, avoid starting your journey until it clears.”
Drivers are also advised to choose main roads where possible, and maintain a firm grip on the steering wheel due to higher winds.
They should also keep an eye out for gaps between trees, buildings or bridges over a river or railway.