Critic Ron Wynn describes Parker as "among Europe's most innovative and intriguing saxophonists...his solo sax work isn't for the squeamish.

Since the 1990s the influence of cool jazz saxophone players has also become apparent in his music, with Parker recording tributes to Warne Marsh and Lee Konitz on Time Will Tell (ECM, 1993) and Chicago Solo (Okka Disk, 1997).

[4] Primarily using the soprano saxophone for these solo performances, the music makes use of a principle known as auditory streaming,[5] where the use of wide registers creates the illusion of polyphony, which Parker terms “pseudo-polyphony”.

Parker has recorded a large number of albums both solo or as a group leader, and has recorded or performed with Peter Brötzmann,[7] Michael Nyman, John Stevens, Derek Bailey, Keith Rowe, Joe McPhee, Anthony Braxton, Cecil Taylor, John Zorn, Fred Frith, Bill Laswell, Ikue Mori, Thurston Moore, Cyro Baptista, Milford Graves, George E. Lewis, Tim Berne, Mark Dresser, Dave Holland, Sylvie Courvoisier, and many others.

Although Parker's focus is free improvisation, he has appeared in conventional jazz contexts, such as Charlie Watts's big band and Kenny Wheeler's ensembles and participated in Gavin Bryars's recording After the Requiem, performing the composition "Alaric I or II" as part of a saxophone quartet.

He also has appeared in pop-music contexts: on Scott Walker's Climate of Hunter, and on dub-influenced albums with Jah Wobble, the adventurous drum n bass duo Spring Heel Jack and rock group Spiritualized.

With Derek Bailey With Han Bennink With Borah Bergman With Paul Bley With Anthony Braxton With Peter Brötzmann With Gavin Bryars With Lawrence Casserley With Alvin Curran With Pierre Favre With Joe Gallivan With the Globe Unity Orchestra With Barry Guy/The London Jazz Composers' Orchestra With the Barry Guy New Orchestra With Paul Haines With Dave Holland With Tony Hymas - Barney Bush With Steve Lacy With Chris McGregor With Roscoe Mitchell With Louis Moholo With The Music Improvisation Company With Natural Information Society With Michael Nyman With Tony Oxley With Jean-François Pauvros With Paul Rutherford and Iskra 1912 With Alexander von Schlippenbach With Manfred Schoof With Setoladimaiale Unit With the Spontaneous Music Ensemble With Spring Heel Jack With David Sylvian with Cecil Taylor With Stan Tracey With Trance Map With Scott Walker With Charlie Watts With Kenny Wheeler With Robert Wyatt