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Stephenson was one of the most in-demand drummers on the British jazz scene in the 1960s.
As a boy, he wanted to become a tap dancer like his idol Gene Kelly, but he was persuaded by his father and his brother to take up the drums.
He already played his first gig in public in the same week as he took his first drum lesson at the age of 14 and was soon working with pianist elder brother Bob's band, and then with the Ray Chester’s Sextet. He went to Birmingham to join the Cliff Deeley Band at the Tower Ballroom, where he played for several months before going on the road.
When he was 16, he joined the singer Lita Roza, a national star who had left the Ted Heath band to tour the variety theatre circuit as a soloist. The 10 months he spent with her was to be of great experience in the music business.
He was conscripted into the Army and served in The Royal Signals Band. He was demobbed in 1957.
Stephenson had a close association with Ronnie Scott and the Club, spent two years in Ronnie Scott's Quartet, and accompanied many visiting stars.
He toured Germany with Tom Jones in 1969 and then took up the resident drum chair with the Kurt Edelhagen Band after moving to Cologne with his wife Jean, daughter Kim, and son Carl. After three years with the Edelhagen band, he teamed up with pianist Paul Kuhn in Berlin and toured all over Europe with a variety of bands and artists.
He joined the Theater des Westens orchestra in Berlin in 1981, and remained there until his retirement on health grounds in 1995.
He also taught at the University of Berlin from 1990 to 1993.
He retired from music on medical advice, and settled in Scotland, where he turned to golf as a restorative, becoming a member of Strathmore Golf Club.
He performed or recorded with Sonny Rollins, Stan Getz, Wes Montgomery, Zoot Sims, Quincy Jones, Paul Gonsalves, Johnny Griffin, Roland Kirk, Gerry Mulligan, Sonny Stitt, Barney Kessel, Benny Golson, Benny Goodman, Nelson Riddle, Ella Fitzgerald, Mel Tormé, Ronnie Ross, Stan Tracey, Ted Heath, Dick Morrissey, Terry Smith, Jack Parnell, John Dankworth, Tubby Hayes, Cleo Laine, Kurt Edelhagen, Peter Herbolzheimer, Horst Jankowski, Paul Kuhn, Rolf Kuhn, Kenny Clarke, Victor Feldman, Heinz von Hermann and Hans Rettenbacher, among many others.
- 1958: Stan Getz and the Big Band of Europe
- 1960: Stan Getz with Kurt Edelhagen Orchestra
- 1962: Bebop from the East Coast - Mike Carr's EmCee Five
- 1964: Boom-Jackie-Boom-Chick - Paul Gonsalves
- 1964: The Night Has A Thousand Eyes - Ronnie Scott and Sonny Stitt - Live At Ronnie Scott's
- 1965: Just Friends - Paul Gonsalves
- 1965: Double Event - Ronnie Scott Trio
- 1965: Wes Montgomery - Live In Europe
- 1965: Wes Montgomery - Live at Ronnie Scott's
- 1965: Three Little Words - The Stan Tracey Quartet with Benny Golson
- 1965: Laughin' And Scratchin' - Stan Tracey
- 1965: "Humphrey Lyttelton And His Band"
- 1966: Alice in Jazz Land - The Stan Tracey Big Band
- 1966: Drum Spectacular - Kenny Clare & Ronnie Stephenson
- 1966: The Stan Tracey Big Band
- 1967: With Love from Jazz - The Stan Tracey Quartet
- 1968: Cleopatra's Needle - Ronnie Ross
- 1969: The Greatest Little Soul Band in the Land - J.J. Jackson
- 1969: Fall Out - Terry Smith -
- 1978: Sincerely Ours - Rolf Ericson/Johnny Griffin