Britton was married on April 8, 1943, in Texas, to Captain Arthur Steel after they met on a blind date arranged by one of her sisters. After the wedding, he was posted to Italy on active Service while Britton remained working at home. They had a daughter, Katherine Lee, born on September 8, 1946. After the war, Steel worked as an advertising executive and went on to manage the Gene Autry hotels (Steel and Autry were first cousins). As their daughter grew up, Britton worked mainly in West Coast theater. She reprised her role in Brigadoon in 1954; appeared in Annie Get Your Gun at the Santa Barbara Bowl; and then returned to Broadway to replace an ailing Janis Paige in Guys and Dolls.
Britton's first role in a major production was as Frank Sinatra's girlfriend in Anchors Aweigh. Afterward, however, came a forgettable part in A Letter for Evie in 1946. She went on hiatus to play the comic role of "Meg Brockie" in the original 1947 production of Brigadoon on Broadway.
After a stint touring with bandleader Don McGuire, Britton's big break came when she was cast as both Celeste Holm's understudy and as Gertie in the Broadway production of Oklahoma!. She played Meg Brockie in the Broadway production of Brigadoon (1947). When Oklahoma! went on tour, she took over Holm's role as Ado Annie.
She returned to the big screen opposite Clark Gable in Key to the City (1950), and then went on to make her most significant film appearance in the classic D.O.A., also in 1950. She made her third film of the year in the Red Skelton vehicle, Watch the Birdie (1951). It was 19 years before she returned to the big screen.
Britton portrayed the title role of the TV version of the Chic Young newspaper comic strip Blondie (1957), opposite Arthur Lake as her husband, "Dagwood Bumstead".
What is perhaps her signature role began in 1963 and lasted until 1966 when she appeared as the nosy and ditzy landlady, Mrs. Lorelei Brown, in My Favorite Martian. After the series ended, Britton appeared in the movies, If It's Tuesday, This Must Be Belgium and Suppose They Gave a War and Nobody Came.
In May 1974, while performing on tour with Don Knotts in The Mind with the Dirty Man, Britton began to have headaches. She was diagnosed with a brain tumor and succumbed within weeks. Britton died in Arlington Heights, Illinois, on June 17, 1974. She was 51. She was survived by her husband, daughter, mother, and sister. Britton is buried at Forest Lawn Memorial Park (Hollywood Hills).