After working, and recording, with Tony Crombie and His Orchestra in 1954, together with leading UK-based jazz musicians such as Crombie, Dizzy Reece, Joe Temperley and Harry South, Kozak went on to join the Vic Ash Quartet which recorded with Maxine Sullivan. He later joined the Don Rendell Sextet (1954–55) and The Ivor and Basil Kirchin Band (1955–56), together with Stan Tracey, and later with the Basil Kirchin Small Band. He would return to record with Tony Crombie in the late 1950s.
Shortly after their return, Kozak started working as an executive at Brian Epstein's NEMS Enterprises as well as managing artists such as Shawn Phillips (1965–67), Donovan (1965 to May 1968), and the duo Michael-Claire (1968).
He produced Marc Brierley's second album for CBS Records Hello (1969), the band Clear Blue Sky (1970–71), and put together the band Tranquility, a “hybrid of pop, rock and English folk music” 1971 - 1974.
Kozak died in 2008.
- 1954: Maxine Sullivan, voc; acc. by Vic Ash Quartet: Vic Ash, cl; Ralph Dollimore, p; Ashley Kozak, b; Ralph Green, d - London
- 1955: Meet Don Rendell - Don Rendell
- 1957: Rockin' with The Rockets - Tony Crombie and His Rockets (Red Morris, Jimmy Currie, Ashley Kozak, Red Mitchell, Clyde Ray) - Columbia 33S 1108
- Heckstall-Smith, Dick and Pete Grant (2004) Blowing the Blues: Fifty Years Playing the British Blues, p. 32. Clear Press Ltd at Google Books. Retrieved 22 May 2013.
- Chilton, John (2004) Who's Who of British Jazz: 2nd Edition, p. 206. Continuum International Publishing Group at Google Books. Retrieved 22 May 2013.
- Thompson, Gordon (2008) Please Please Me: Sixties British Pop, Inside Out, p. 87. Oxford University Press, 10/09/2008 at Google Books. Retrieved 22 May 2013.
- Credits allmusic. Retrieved 22 May 2013.