Born in The Chalfonts in Buckinghamshire, England, he began acting on the Broadway stage in 1924 and went on to appear in thirty more Broadway plays over the next four decades. He first acted in Hollywood films in 1930, debuting in director Mack Sennett's The Chumps. In his career he appeared in more than forty movies and also made more than forty guest appearances on television shows. He was part of the regular cast for the 1967 season of the family comedy, Family Affair.
Outside his movie career, Williams gained fame as the star of a television commercial for 120 Music Masterpieces, a four-LP set of classical music excerpts from Columbia Records. This became the longest-running nationally seen commercial in U.S. television history, for 13 years from 1971 to 1984. It began, "I'm sure you recognize this lovely melody as 'Stranger in Paradise.' But did you know that the original theme is from the Polovetsian Dance No. 2 by Borodin?" The commercial became so familiar that it was spoofed by Charles Rocket on Saturday Night Live.
In 1953 Williams was awarded a Tony Award for Best Supporting or Featured Actor (Dramatic) for his role as Chief Inspector Hubbard in "Dial M for Murder" on Broadway. When Alfred Hitchcock took over the script to make a movie of the play in 1954, he cast Williams for the same role.
Williams also played in several episodes of Alfred Hitchcock Presents on TV, including "The Long Shot" with Peter Lawford (November 27, 1955), "Back for Christmas" (1956) , "Whodunit" (1956), "Wet Saturday" (1956), the 3-part episode "I Killed the Count"(1957), and "Banquo’s Chair" (1959).
He was educated at Lancing College.