The warning will remain in place until 6am on Tuesday as some areas will experience 30-50mm of rain in 3 hours. According to the meteorological service there will be frequent lighting and gusty winds.
The area affected by the warning stretches from the Isle of Wight to North Norfolk and includes London.
It is likely that the storms could cause some disruption, according to the Met Office.
This could include the fact that driving conditions are likely to be affected by spray, standing water and hail.
As a result, bus and car journeys could take longer than they normally do.
There is also the possibility of damage to buildings from lightning strikes.
Train services could also be delayed.
Flooding could also affect some homes and businesses with some damage to buildings and structures possible.
It is also possible that there could be some short term loss of power.
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During the storm itself people should avoid using the landline phone and playing golf.
They said: “Telephone lines can conduct electricity so try to avoid using the landline, unless in an emergency.
“If outside, avoid water and find a low-lying open place that is a safe distance from trees, poles or metal objects.
“Avoid activities such as golf, rod fishing or boating on a lake.
“Be aware of metal objects that can conduct or attract lightning, including golf clubs, golf buggies, fishing rods, umbrellas, motorbikes, bicycles, wheelchairs, mobility scooters, pushchairs, wire fencing and rails.
“If you are in a tent, try to stay away from the metal poles.
“If you find yourself in an exposed location it may be advisable to squat close to the ground, with hands on knees and with head tucked between them.
“Try to touch as little of the ground with your body as possible, do not lie down on the ground.
“If you feel your hair stand on end, drop to the above position immediately.”