Firefighters, ambulances, and police were all called to the incident in Myrtle Road at around 1am.
An East Sussex Fire and Rescue Service (ESFRS) spokesperson said, “Crews used one hose reel and one hose reel jet to extinguish the fire.
“SECAmb also attended due to one person suffering from smoke inhalation.
“The cause of the fire was deemed to have been deliberate and the incident was handed over to Sussex Police.”
A Sussex Police spokesperson said, “Police were called by ESFRS at 1.05am on Thursday (July 23) following a car fire in Myrtle Road.
“The fire is thought to have been started deliberately, and enquiries are ongoing.
“Anyone who witnessed the fire, saw any suspicious behaviour in the area at the time, or anyone who may have any other information about the matter, is asked to contact police online or by calling 101 quoting serial 70 of 23/07.
“Alternatively, you can call the independent charity Crimestoppers anonymously on 0800 555 111.”
A South East Coast Ambulance (SECAmb) spokesperson said one ambulance attended the scene, which was there for about an hour, but no-one required hospital treatment.
It is the fifth deliberate fire in the space of two weeks in this area of Eastbourne.
Three blazes at the Alexandra Arms in Seaside are being investigated as arson attacks by police, as well as a fire at a disused property in nearby Fort Lane.
Serious damage was caused to the buildings in these fires, but no one was reported as harmed.
Detectives are appealing for witnesses to the incidents.
Contact police online or by calling 101 quoting serial 130 of 11/07.
Alternatively, you can contact the independent charity Crimestoppers anonymously on 0800 555 111.
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