A crew from Shoreham was sent to tackle the flames in Kingston Broadway, near the Holmbush Centre, at around 8.30am.
A spokesman for the fire service said the car was ‘well alight’ when firefighters arrived.
Two hose reels and two breathing apparatus were used to tackle the blaze.
The fire is being treated as an accident.
The spokesman added the roundabout exit onto Kingston Broadway has been closed due to the fire.
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