Straker was born in Jamaica, and moved to London in his early childhood. He first became known in 1968, when he starred as Hud in the original London production of Hair. Over the next three years, he released a succession of singles on the Polydor label, though none became commercially successful. In 1971 (credited mononymously as Straker), he appeared in the comedy-drama film Girl Stroke Boy, co-written and co-produced by Caryl Brahms and Ned Sherrin.
In 1972, he signed with RCA Victor, and had a minor hit with the song "The Spirit is Willing", based on "Jesu, Joy of Man's Desiring" by J. S. Bach, and adapted by the songwriting duo of Ken Howard and Alan Blaikley, who also produced the single. Credited to "Peter Straker – The Hands of Dr. Teleny", it entered the charts on 19 February 1972, had a chart life of 4 weeks and peaked at No.40. Howard and Blaikley wrote and produced Straker's first album in 1972, Private Parts, based around Straker's reminiscences of his life.
In the mid-1970s he moved to Pye Records, and toured as a singer. He met Freddie Mercury, and they became close friends. Mercury was instrumental in winning Straker a new recording deal with EMI, and co-produced his first album for the label, This One's On Me, with Roy Thomas Baker. Straker's 1978 album, Changeling, produced by Tim Friese-Greene, with most of the songs written by guitarist Mike Allison though several were written or co-written by Straker. In 1979, Straker released the album Real Natural Man, released on Rocket Records. However, the record again found little success, and Straker reconsidered his career direction.