During her career she served at the University of London Observatory, Yerkes Observatory of the University of Chicago, Cavendish Laboratory in Cambridge, England, the California Institute of Technology, and from 1979 to 1988 was first director of the Center for Astronomy and Space Sciences at the University of California at San Diego (UCSD), where she worked from 1962 on.
In 1950, she applied for a grant at the Yerkes Observatory in Williams Bay, Wisconsin, and went to the United States in 1951. She went back to England in 1953 and started research in collaboration with her husband Geoffrey Burbidge, Fred Hoyle and William Alfred Fowler. The resulting theory was called the B2FH theory after the participants.
After ten years, in 1955, she finally gained access to the Mount Wilson Observatory, posing as her husband's assistant. When the management found out, they eventually agreed that she could stay, if she and her husband went to live in a separate cottage on the grounds rather than using the men's dormitory.
Her 1972 directorship of the Royal Greenwich Observatory was also the first time in 300 years that that directorship was not associated with the post of the Astronomer Royal, which was given to radio astronomer and later Nobel prize winner Martin Ryle instead. She left this post in 1974, fifteen months after accepting it, when controversy broke out over moving the telescope in the Observatory to a more useful location.
Experiences such as these turned Burbidge into one of the foremost and most influential personalities in the fight to end discrimination of women in astronomy. Consequently, in 1972 she turned down the Annie J. Cannon Award of the American Astronomical Society because it was awarded to women only: "It is high time that discrimination in favor of, as well as against, women in professional life be removed".
In 1976, she became president of the American Astronomy society, and in 1977, became a United States citizen. In 1983 she was elected president of the American Association for the Advancement of Science; she has also served as vice-president and president of the American Astronomical Society.
In 1957, the B2FH group showed the famous result that all of the elements except the very lightest are produced by nuclear processes inside stars. For this they received the Warner Prize in 1959. In her later research she was one of the first to measure the masses and rotation curves of galaxies and was one of the pioneers in the study of quasars.
At UCSD she also helped develop the faint object spectrograph in 1990 for the Hubble Space Telescope. Currently, she is a professor emeritus of physics at UCSD and continues to be active in research, i.a. engaging in non-standard cosmologies like intrinsic redshift
Named after her