Born in Boston in 1933, Loudon attended the American Academy of Dramatic Art in New York and first gained popularity as a regular on Gary Moore's TV variety show. She made her Broadway debut in the short-lived 1962 musical Nowhere to Go But Up, then went on to appear in Noël Coward's Sweet Potato, The Fig Leaves Are Falling (for which she received a Tony nomination), Three Men on a Horse, and The Women. Following her great success in Annie, Loudon earned another Tony nomination for her performance as Bea Asher in Ballroom (in which she sang "Fifty Percent") and replaced Angela Lansbury as Mrs. Lovett in the original production of Sweeney Todd.
She later appeared in The West Side Waltz (with Katharine Hepburn), Noises Off, and Jerry's Girls. Her last Broadway appearance was as Carlotta Vance in one preview performance of Lincoln Center Theater's revival of Dinner at Eight, after which Loudon withdrew and was replaced by Marian Seldes.