The Environment Agency has issued a flood alert for the River Exe between Exe Bridges and Tiverton.
A statement said: “Rivers are responding to last night’s rainfall and are rising quickly.
“Rain has now cleared the area but rivers will continue to rise. A further 15 millimetres rainfall is forecast during today.”
At noon there were 35 flood alerts in place across the South West, including one for the River Clyst.
Residents were being told to keep a careful eye out at riverside locations and roads between Broadclyst and Clyst St. Mary, including Broadclyst, Ashclyst, Clyston Mill, Sowton Barton, Newcourt Barton, the A3052 at Clyst Honiton, and the B3181 at Broadclyst.
A spokesman for the Environment Agency said: “People should take extra care if they are driving on these roads.
“If there is surface water they should reduce their speed and not enter flood water.”