A 38-year-old man was driving a black C180 Compressor Mercedes towards Dodgson Road in Preston when he was approached by four men on bikes and two men on foot.
One of the men began to punch the driver through the car window whilst the others threw their bikes in front of the car.
After an altercation, the driver, his 32-year-old girlfriend and 39-year-old brother got out of the car, which was driven off by one of the gang.
A spokesman for Lancashire police, who released the information on Saturday, said: "I would like information about who these lads are.
"There were quite a lot of people around at the time of the incident which happened on Sunday July 27 at 6.20pm.
"Anyone can contact us with information, in confidence, and we will not force them into making witness statements."
The man who initially approached the car is described as being as white, aged about 18, with mousy blond hair with a centre parting in the fringe, with a prominent nose, approximately 5ft 7in.
The man who stole the car is described as being aged about 18, with brown hair which was short round the sides and spiky on the top, clean shaven and of medium build.
The vehicle, which was a courtesy car, was recovered in Grimsargh on Saturday (August 2).