The Met Office has issued an amber weather warning, with strong south westerly winds expected to develop during Wednesday afternoon, spreading along the south coast from Cornwall and reaching Kent later in the evening.
Road users are advised to check the weather forecast and road conditions before travelling and gusts are expected to reach 55 to 65 mph inland.
The Shoreham flyover has been highlighted as one of the exposed routes which could see gusts up to 75 mph from 9pm onwards and there is expected to be a strong crosswind.
Heavy rain overnight and into Thursday will further affect driving conditions, with spray reducing visibility.
Rob Llewellyn, an emergency planner at the Highways Agency, said: “High winds can affect any section of road, especially exposed roads and high bridges. Be alert for sudden gusts of wind, and give high-sided vehicles, caravans, and motorbikes plenty of space.
“We would urge road users to play their part by checking weather forecasts and traffic conditions before they set out and drive with extra care.”