An English singer and songwriter, best known for her involvement with the British folk rock movement, including two spells as a member of Fairport Convention, as well as her duet with Robert Plant on Led Zeppelin's 4th album in 1971 on The Battle of Evermore.

Born in Merton Park, she studied classical piano as a child. Her Scottish grandmother was a singer of traditional songs and at an early age, Denny showed an interest in singing, despite the disapproval of her extremely strict parents.

After leaving school, she started training as a nurse at the Royal Brompton Hospital. In 1965, she enrolled at the Kingston College of Art in London, 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 with them in Denmark. The album includes an early version of her best-known (and widely covered) song, Who Knows Where the Time Goes. Judy Collins recorded the song, helping to bring Denny to attention. Denny also recorded her first solo album in this period, featuring traditional songs and covers of folk contemporaries.

In 1968, Denny became the lead vocalist for Fairport Convention (replacing Judy Dyble), recording three albums with them. Denny is credited with encouraging Fairport Convention to explore the traditional British folk repertoire and is thus a key figure in the development of British folk rock.

Denny left Fairport Convention in 1969, after recording and, very briefly, touring their release Liege & Lief. She went on 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. The North Star Grassman and the Ravens and Sandy remain her most popular solo albums.

In 1973, she married Lucas and returned to Fairport Convention for a world tour and another album, Rising for the Moon, featuring several of her own compositions. During her solo period, Denny appeared in a brief cameo on Lou Reizner's version of the Who's rock opera, Tommy, and duetted memorably with Robert Plant on The Battle of Evermore from Led Zeppelin's 1971 album (Led Zeppelin IV). 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 gained a devoted cult following, but remained deprecating of her talent and unsure of her true direction. Some of her best-loved recordings are interpretations of British traditional songs. Denny herself was unsure as to whether she wanted to continue in that vein (in the manner of Steeleye Span and Maddy Prior) or that of a singer-songwriter like Joni Mitchell. She also had yearnings for success in the mass market, for which her shy, unpredictable nature and insecurity about her looks were ill-suited. Her solo albums feature efforts in all three directions, gaining her a reputation for charming eclecticism rather than the star power she and Lucas craved.

Her charisma and extraordinary alto voice were never in doubt. Unfortunately, the stress of the Fairport Convention world tour in 1973 helped to make it apparent that Denny's heavy drinking and smoking were damaging her voice, inclining her to put elaborate string arrangements on her last two solo albums (Like an Old-Fashioned Waltz and Rendezvous). These heavily produced albums were not as well received by the critics.

Denny began to question her career goals in earnest and decided to turn her attention to raising a family. At the same time, her substance abuse became critical and her behaviour, always erratic, became sufficiently trying to alienate most of her fellow musicians, including Lucas and her other colleagues in Fairport Convention.

Denny died of a cerebral haemorrhage on 21 April 1978 after falling down a flight of stairs. The exact circumstances of her death are somewhat murky. Denny was only 31.