Goossens was the principal harpist of the BBC Symphony Orchestra for 50 years. She was one of the first women to tour with the London Symphony Orchestra, and was both the first harp soloist to make a radio broadcast (in 1924) and the first to appear on television (in 1926).
Her last performance was in 1991, shortly before her 92nd birthday, as an accompanist to Gwyneth Jones at the Last Night of the Proms. Afterward, she continued to teach. Goossens was quite involved with new music, playing frequently with the London Sinfonietta and the Fires of London. A 1999 concert in her honor, at which she sat in the Royal Box of the Royal Festival Hall, featured a program of works by Schoenberg, Berg, and Webern as a tribute to her involvement with such composers.
Goossens' grandfather and father, both named Eugene Goossens, came to England from Belgium in the late 19th century. Both were conductors at the Carl Rosa Opera Company. Goossens' brother, also named Eugene, was the conductor of the Sydney Symphony. Her other siblings played oboe, horn, and harp.