Southern Water announced restrictions from Friday for customers in Hampshire and on the Isle of Wight, while the measure will follow exactly a week later for South East Water customers in Kent and Sussex.
Mr Dewhurst also urged people to follow precautions in the warm weather to avoid becoming overheated, including closing curtains and windows during the day.
“As the heatwave develops, keep out of the midday sun, try and stay in the shade if you are outside and the best thing to do is close the curtains during the day and then open the curtains and windows at night to let the cooler air in,” he said.
“Drink lots of water and make sure to stay hydrated.”
He added: “Overall Augusts tend to be a wetter month so it is fairly unusual to have prolonged dry weather over August.”