Sheldon was born into a family of carnival businesspeople, and he worked as a barker while receiving training in acting. After completing military service, he landed a role in the 1961 film The Guns of Navarone and worked in small theatre productions.He shared a flat in London with three other unknown actors-including Michael Caine and Sean Connery He was discovered by Bunny Lewis while performing onstage, and was quickly offered a recording contract with Decca Records, even though he had no previous experience performing as a singer.
Sheldon's first single was "Book of Love", which did not chart. The follow-up single was a cover of the tune "Runaround Sue", which became a hit record in the UK reaching No. 36 in the charts, although Dion's version soon outstripped it in popularity both in the UK and the United States. His next single, "Your Ma Said You Cried in Your Sleep Last Night", became his highest charting hit at No. 29. Shel Talmy produced the next single, "Lollipops and Roses", which flopped, but with the tune "I Saw Linda Yesterday" he managed to crack the UK Singles Chart for the last time in 1963 at No 36.
After the middle of the decade, Sheldon returned to a career in acting, where he appeared on TV in Doctor Who, The Avengers and Triangle, and in films such as The Yellow Teddy Bears, Ryan's Daughter and Appointment with Death. He also published novels. In 2007, his entire Decca discography was released on CD by Vocalion Records.
- "Book of Love" (1961)
- "Runaround Sue" (1961) UK #36
- "Your Ma Said You Cried in Your Sleep Last Night" (1962) UK #29
- "Lollipops and Roses" (1963)
- "I Saw Linda Yesterday" (1963) UK #36
- "Mickey's Monkey" (1964)