The man had been in the McDonald’s branch around 4.45pm on Friday evening (January 25) when a verbal altercation occurred and staff asked him to leave, police said.
He did so, but returned around 6.20pm and started a small fire outside the premises, which was attended by East Sussex Fire and Rescue, confirmed police.
No one was injured and the fire was quickly extinguished, according to police.
Police describe the suspect as white, 5ft 10-5 or 11ins, of slim build and wearing a green jacket, jeans and a maroon or brown beanie hat with white writing on the front.
A spokesman said: “If anyone witnessed the incidents either inside the McDonald’s or outside please report online or call 101 quoting serial 989 of 25/01.”