Taylor was born in Hampstead, a wealthy district of north-west London, the second child of Francis Lenn Taylor (1897–1968) and Sara Viola Warmbrodt (1895–1994), who were Americans residing in England. Taylor's older brother, Howard Taylor, was born in 1929. Her two first names are in honor of her paternal grandmother, Elizabeth Mary (Rosemond) Taylor. Taylor was born both a British subject and an American citizen, the former by being born on British soil under the principle of jus soli, and the latter through her parents under the principle of jus sanguinis.

Both of her American parents were originally from Arkansas City, Kansas. Her father was an art dealer and her mother a former actress whose stage name was Sara Sothern. Sara retired from the stage when she and Francis Taylor married in 1926 in New York.

At the age of three, Elizabeth began taking ballet lessons with Vaccani. Shortly after the beginning of World War II, her parents decided to return to the United