As a child Denny studied classical piano. She left school before taking A-levels and started to train as a nurse at Brompton Chest Hospital. In 1965 she enrolled at Kingston School of Art, where she became involved in the folk club on campus. It was there that she met fellow students John Renbourn and Eric Clapton. She travelled in to Earls Court to play at the Troubadour club, where a member of The Strawbs heard her. In 1967 she was invited to join the band and recorded one album in Denmark with them, including the earliest version of her best-known (and widely covered) song "Who Knows Where the Time Goes." In 1968 she became lead vocalist for Fairport Convention replacing Judy Dyble, recording three albums with them. Denny is credited with introducing the band to the traditional British folk repetoire, and is thus a key figure in the development of British folk-rock.

Denny left Fairport in 1969, just before the release of Liege and Lief, to form her own band, Fotheringay, including her boyfriend, Australian born Trevor Lucas. She dissolved the group after one album to record solo albums, with several members of Fairport Convention as guests. In 1973 she married Lucas and returned to Fairport for a world tour and another album, Rising for the Moon, containing several of her own compositions.

During her solo period Denny appeared on Lou Reitzner's version of The Who's rock opera Tommy and on Led Zeppelin's 1971 album Led Zeppelin IV. She was voted "Female singer of the year" by Melody Maker in 1970 and 1971. Together with contemporaries including Richard Thompson and Ashley Hutchings, she participated in a one-off project called "The Bunch", recording a collection of rock standards. She died of a cerebral haemorrhage in 1978 after falling down a flight of stairs. After her death Trevor Lucas returned to Australia with their daughter Georgia. He died in 1989 of heart failure.

There is a biography, Sandy Denny: No More Sad Refrains, by Clinton Heylin.