Bennett was born in Garnant, Carmarthenshire, Wales, the son of Sarah Gwen (née Lewis) and Gorden Bennett. He was the brother of actor Alun Lewis, who is best known for playing Vic Windsor in Emmerdale. Bennett was brought up in London from an early age, and attended Sunnyhill School, Streatham, Henry Thornton Grammar School, Clapham (1955–62) and the Royal Academy of Dramatic Art.