The national weather agency has issued a yellow warning for South West England.
It states that while many places will remain dry, those that see rainfall could witness 20-30 mm in an hour and up to 50 mm in two to three hours, as well as lightning.
The Met Office warns that driving conditions will likely be affected, as well as possible delays to train services.
It also warns of possible short-term loss of power and other services.
The agency adds: “Some flooding of a few homes and businesses likely, leading to some damage to buildings or structures”.
Buildings may also be damaged by lightning strikes.
A map released by the Met Office shows the storms will sweep across Cornwall up to Plymouth and Exeter.
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.