Born in London, the son of salesman in the steel industry, Dignam grew up in Sheffield and was educated at the Jesuit College where he appeared in numerous Shakespearean plays. He learned his craft touring England and America with Ben Greet's Shakespeare company. His range extended from the Louis Macneice radio play, The Dark Tower in the 1940s to the TV thriller, The XYY Man in the late 1970s. Dignam was married three times, divorced twice (his character in The XYY Man frequently complains about the expense of maintaining multiple ex-wives).