Martin studied classical saxophone at Trinity College of Music.

At that time there were no jazz courses in London, so he met some other jazz musicians at the college, including pianist Simon Purcell, saxophonist Mark Lockheart and the future members of saxophone quartet Itchy Fingers. He toured Europe, South America, Africa and the USA with this group, appearing at major jazz festivals and playing on their first two CDs. In 1986 they won the Schlitz Young Jazz Musicians of the Year Award.

Since 1988, Martin's main band has been the Martin Speake Group, which has recorded albums In Our Time and Trust. Other projects include two very different duos with guitarist Phil Lee (exploring the jazz standard) and pianist Nikki Iles (playing contemporary tunes and free improvisation) and the seven-piece world music band Fever Pitch featuring three percussionists. He also plays the music of Ornette Coleman with Mind and Time, free improvisation with the Eternal Triangle and Indian music with Dharambir Singh.

Martin has also performed with Paul Motian, Bobo Stenson, Loose Tubes, Stan Tracey, Bhavani Shankar, Billy Jenkins, Django Bates, Bob Wilber, Conrad Herwig, Don Weller, Ronan Guilfoyle, Alison Bentley, The Style Council, Ann Pigalle, Kadam, John Williams, Airto Moreira and Flora Purim, Jim Mullen, Dave Cliff, Julian Arguelles, Ephie Resnick and the Royal Shakespeare Company among others. He is very involved in jazz higher education and has also taught in schools, adult education classes, weekend courses and summer schools throughout the country. He has also composed music for the Associated Board jazz piano syllabus and a solo saxophone piece for Faber Music.