The assault happened at the Smith and Western bar and grill in Boxhill Road, Box Hill, at about 9pm on October 13 when a customer refused to pay his bill, picked up a glass from the bar and threw it at the victim.
The male member of staff required hospital treatment for cuts and grazes to his face and mouth.
Detective Constable Leigh Wall, of Epsom CID, said: "This was a vicious and unprovoked attack which left the victim with facial injuries but could have had far more dire consequences."
The group consisted of two men, two women, a teenage boy and a young baby.
The suspect who assaulted the member of staff is described as a white man, aged in his late 20s or early 30s, of slim build, around 5ft 10in tall with short, brown hair.
He was wearing a grey jacket with black writing on the front.
The other man was in his mid to late 20s, also of slim build, around 5ft 8in tall with blond, spiky hair. He was wearing a T-shirt and dark jeans.
The two women were described of similar age, around 5ft 6in tall and with brown hair. One was wearing a white T-shirt and blue jeans and was heavily pregnant.
The teenage boy was around 16 years old, with short, ginger hair and was wearing a top with horizontal stripes.
Anyone who has any information should contact Epsom CID on 0845 125 2222, quoting reference MV/09/4733.