Greif was born in Sawbridgeworth, Hertfordshire, England, in a building originally belonging to Anne Boleyn as a gift from King Henry VIII. He was educated at Sloane Grammar School, where he was school champion in athletics and swimming and represented the school and the county in athletics at the White City Stadium amongst other locales. He briefly attended the Regent Street Polytechnic before entering a variety of jobs including trouble shooter at a TV and radiogram manufacturer and as a negotiator in a boutique West End estate agency before applying for drama school.
