He was born in Adelaide, South Australia, and initially played classical percussion in the Adelaide Conservatorium of Music, before teaching himself the guitar. In 1967 Peek formed a Psychedelic pop, progressive rock group, James Taylor Move but left by May 1968, moving to London. He returned to Adelaide, Australia, to join a newly formed rock band Quartet which, despite a contract from England's Decca Records, proved artistically unsuccessful. An Australian single "Now"/Will My Lady Come" [Decca Y-8977] was released in 1969. The A-side is credited to Britten; the B-side to Spencer, Tarney and Peek. For a time, following their move to London, he and his fellow Adelaide-born bandmates—guitarist Terry Britten, bassist Alan Tarney, and drummer Trevor Spencer—made their livings as session musicians together, playing with everyone from the New Seekers and Mary Hopkin (Earth Song, Ocean Song) to Cliff Richard, whose regular backing band they became on stage and on record during the 1970s. Peek also worked with Manfred Mann, Lulu, Tom Jones, Jeff Wayne (War of the Worlds), and Shirley Bassey, among others. He wrote the music for the internationally broadcast "Singapore Girl" television advertisements for Singapore Airlines.
In 1979, he joined the classical/progressive rock quintet Sky. In association with classical guitarist John Williams, keyboardist Francis Monkman, bassist Herbie Flowers, and drummer Tristan Fry, Peek played on seven studio albums with the band, before departing in 1985. Peek recorded three albums—Guitar Junction, Awakening, and Life & Other Games— but achieved greater prominence through his work with Sky and his session work with Olivia Newton-John, Kiki Dee, Sally Oldfield, the Alan Parsons Project, and the London Symphony Orchestra (in association with Francis Monkman on their Symphonic Rock: British Invasion releases). He also played on various soundtracks, including Monkman's music for The Long Good Friday.
Following a failed business venture and bankruptcy, in 2010 he was prosecuted in Perth, Western Australia on two counts of making a false statement to deceive or defraud. A full trial was originally scheduled for 2011, later adjourned until 2012  and ultimately never took place.
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- Neale Prior (30 March 2002). "Sky was the limit: Peek has a second crack at bankruptcy". Sydney Morning Herald. Retrieved 12 December 2012.
- Cordingley, Glenn (2010-07-29). "Former rock star Kevin Peek faces Perth Court". Perth Now. Retrieved 2013-02-18.
- Mark Russell (2011-10-30). "Pop star to stand trial over fraud". Melbourne: The Age. Retrieved 2013-02-18.
- "Former rock guitarist Kevin Peek to fight $8 million fraud charges" - article by Phil Hickey in Perth Now, 2 November 2011.
- Rania Spooner (2013-01-25). "Kevin Peek | death". Melbourne: The Age. Retrieved 2013-02-18.