The owners say they are touched by how the Seaford community has rallied around them.
The vehicle fire spread to shops in Sutton Road in Seaford, causing significant damage, says police.
East Sussex Fire and Rescue Service is urging people to avoid the area while firefighters work.
Fire services are urging the public to only call 999 in an emergency after reports about neighbours.
East Sussex Fire and Rescue Service says nobody was injured in the fire in Lenham Avenue, Saltdean.
Two fire engines and two four-by-four vehicles were sent to the scene in Pevensey.
The fire is ruled an accident by East Sussex Fire and Rescue Service.
Fire services in Sussex, Surrey and Kent have all issued advice on how to help with prevention.
Steven Conisbee, from Fetcham, says the speed at which flames engulfed his land was "alarming".
