Professor Stowell was educated at the University of Cambridge (MA, PhD) and at the Royal Academy of Music, London (Recital Diploma, Marjorie Hayward Prize). He made his London solo debut as a violinist at the Purcell Room in 1974 and has performed throughout the UK as a soloist and chamber musician. He was also, for many years, a member of The Academy of Ancient Music, The English Concert and other period-instrument ensembles. In addition, he has participated in numerous radio and television broadcasts, as well as commercial recordings (Decca/L'Oiseau Lyre). Professor Stowell came to Cardiff as Lecturer in Music in 1976, becoming Senior Lecturer in 1984 and Professor in 1988, Acting Head of School (1994–96 and 1999) and Head of School (2000–2008). He was appointed an ARAM in 1990 and a Fellow of the Learned Society of Wales in 2012.
Professor Stowell has served as an assessor and consultant both within the university and conservatoire sectors and also for the HEFCE, the WJEC and grant-awarding bodies such as the AHRC (Music Review Panel, 2005), British Academy and Leverhulme Trust. He has also been a consultant to the NYO of Great Britain and has been a jury member for various competitions, including BBC Young Musician, Live Music Now and Young Musician of the Gulf (Bahrain). He has been a performance adviser for several 'period' ensembles and has participated in the outreach work of The Orchestra of the Age of Enlightenment, the English Symphony Orchestra and the Welsh Sinfonia. He is co-editor of the Cambridge Handbooks to the Historical Performance of Music, a regular assessor for major publishing houses and journals, and a member of both the Advisory Committee for the publication of the Complete Works of Francesco Geminiani, and the Research-Editorial Council for the Henryk Wieniawski Collected Edition. He participated as co-investigator in a collaborative AHRC-funded project entitled 'Nineteenth- and early twentieth-century annotated editions of string music: bibliographical problems, editorial content and implications for performance practice' with the School of Music, University of Leeds (2008–12). From 2010, he has served as mentor to Claire Holden, AHRC Fellow in the Performing and Creative Arts. In 2004, he established the Centre for Research in Historically Informed Performance (CRHIP), of which he is director.