Beck was born in Brixton, London, and attended Pinner County Grammar School—the school Reg Dwight (Elton John) and Simon Le Bon would later attend. He studied piano in his youth, but decided to go into a career as an engineering technical draughtsman. Largely self-taught, he returned to music after spending time in Canada where he was exposed to the works of George Shearing and Dave Brubeck.
He joined the Tubby Hayes group in 1962 back in England he and later formed his own trio, made up of Tony Oxley, Jeff Clyne, and himself. From 1969 to 1972 he toured with Phil Woods's European Rhythm Machine.