Matthew studied at Kings College, Cambridge, and at the National Opera Studio, and in 1982 won the Decca-Kathleen Ferrier Prize. At the outset of his career, he sang as a principal bass with The Royal Opera, Covent Garden, and as a guest with many other companies, and in recent years he has moved into the bass-baritone and Heldenbariton repertory. This process reached a significant landmark when he sang the role of Wotan/The Wanderer in Scottish Opera's new production of Der Ring des Nibelungen, first seen at the Edinburgh International Festival.

Other engagements have included Kurwenal Tristan und Isolde with La Monnaie, Don Pizarro Leonore under Gardiner at the Proms, Salzburg Festival, Concertgebouw, Amsterdam and the Lincoln Center Festival, New York; Swallow Peter Grimes for ROH; Siegfried and Die Walkure and Orest Elektra in Stuttgart; Wotan Siegfried Opera de Lyon; the title role in The Flying Dutchman, Opera de Rouen; Vairochana in the world premiere production of Jonathan Harvey's Wagner Dream in Luxembourg, Amsterdam and Paris; Peneios Daphne for his debut with Santa Fe Opera, followed by Tsargo Adrianna Mater in 2008; Scarpia Tosca, Amfortas Parsifal, Kurwenal, Don Pizarro Fidelio for Scottish Opera; Count Walter Luisa Miller and Scarpia for Opera North; Wotan The Rhinegold, Ramfis Aida, Swallow Peter Grimes, King Marke Tristan und Isolde, Jochanaan Salome for English National Opera; Cadmus The Bassarids at the Chatelet, Paris and in Cologne; Jochanaan and Mr. Flint Billy Budd with LSO/Richard Hickox; and Pizarro Fidelio (concert performances) with both the CBSO and the Swedish Chamber Orchestra. On concert platform he has sung The Dream of Gerontius, Beethoven 9, Shostakovich 14, Elijah, the Verdi Requiem, Berlioz's L'Enfance du Christ, and Mahler 8 with orchestras in the UK and Europe.

His various recordings include Beethoven's Leonore, Berlioz' L'enfance du Christ, Britten's Billy Budd and Peter Grimes, Elgar's The Dream of Gerontius, Falla's El Retablo di Maese Pedro, Menotti's Martin's Lie and Rossini's Il barbiere di Siviglia.

Matthew also gained a high reputation in conducting, of which include his long-standing association with The Corydon Orchestra and Singers, of which he is founder and artistic director. His many notable recordings with them include highly acclaimed performances of Bruckner's Masses and Te Deum, Berlioz' L'Enfance du Christ and Vaughan Williams' opera Hugh the Drover. His guest conducting includes appearances with the English Chamber Orchestra, BBC National Orchestra of Wales, the Northern Sinfonia, London Mozart Players, City of London Sinfonia, Royal Seville Symphony Orchestra, the RTE Concert Orchestra, The Manchester Camerata and The Hanover Band (where he was Principal Conductor for the 1998/99 season).

Engagements in 09/10 season include Pizzaro Fidelio in concert with the Rotterdam Philharmonic and Valery Gergiev, Sparafucile Rigoletto, Messiah with the Orquesta Sinfonica de Gran Canaria, Peneios Daphne for Oper Frankfurt and La Roche Capriccio for Grange Park Opera.