Between 1964 and 1975 he was Head of Physical Education in three schools, took a Masters in Recreation Management and was a Senior Regional Officer with the Sports Council. He studied singing with Bruce Boyce in London at the same time and made his professional operatic début with Scottish Opera in 1975.

He was a Principal of English National Opera from 1978 - 1985 and has also sung with The Royal Opera Covent Garden, Glyndebourne Festival Opera, Opera North, Welsh National Opera and Northern Ireland Opera in the UK.

He has had an extensive international career since 1976, including 16 seasons and over 120 performances at the Bayreuther Festspiele (Loge and Mime, Der Ring des Nibelungen - two productions; David, Die Meistersinger; Steuermann, Der fliegende Holländer; Melot and Seemann, Tristan und Isolde). 1981 - 2004; 15 seasons at The Metropolitan Opera, New York (Loge and Mime, Der Ring des Nibelungen; Bégearss, The Ghosts of Versailles - world première; Captain Vere, Billy Budd; Steva, Jenufa; Herodes, Salome; Hauptmann, Wozzeck - two productions; Gregor, The Makropulos Case; Prinz/Marquis, Lulu; Tanzmeister, Ariadne auf Naxos). 1985 - 2010; many performances in Aix-en-Provence, Amsterdam, Barcelona, Berlin (Deutsche Oper, Deutsche Staatsoper), Bilbao, Biwako, Bonn, Brussels, Catania, Chicago, Dallas, Dublin, Frankfurt, Geneva, Hamamatsu, Hamburg, Los Angeles, Luxembourg, Madrid (Teatro Real, Teatro de la Zarzuela), Matsumoto, Milan La Scala, Munich, Nagoya, Nice, Paris (Opéra Bastille, Théâtre des Champs Élysées, Théâtre du Châtelet, Palais Garnier), Rome, Salzburg, San Francisco, Seville, Stockholm, Tokyo, Toronto, Toulouse, Turin, Vancouver, Vienna (Staatsoper), Yokohama, Zurich. 1976 - 2014; over 385 Wagner performances including over 275 performances of Der Ring des Nibelungen. 1977 - 2014 and his début as an actor at the Grand Théâtre Luxembourg reciting Plato’s Apology, The Trial of Socrates. 2011.

Graham has recorded with BBC, BMG, Challenge Classics, Chandos, Decca, Deutsche Grammophon, EMI, Erato, Etcetera, EuroArts, Oehms Classics, Opera Rara, Opus Arte, Philips, Profil, Sony, Teldec, The Met, New York, United Artists and Warner Classics.

His DVDs include Die Meistersinger von Nürnberg, Der fliegende Holländer, Der Ring des Nibelungen (Bayreuther Festspiele); The Ghosts of Versailles, Wozzeck (The Metropolitan Opera, New York); Der Ring des Nibelungen, Lady Macbeth of Mtsensk, Khovanshchina (Gran Teatre del Liceu, Barcelona); Der Ring des Nibelungen (De Nederlandse Opera, Amsterdam); The Makropulos Case (Canadian Opera, Toronto); Ariadne auf Naxos (Opéra National de Paris); Wozzeck (Deutsche Staatsoper, Berlin); The Rake’s Progress (Glyndebourne Festival Opera).

He has sung in many international music festivals including Amsterdam, Antwerp, Bamberg, Berlin, Brussels, Canaries, Chicago, Cologne, Copenhagen, Edinburgh, Lucerne, Milan, Paris, Rome, Tel Aviv, Washington and the London Proms.

He was nominated ‘Outstanding Individual Achievement in Opera’, including an American Emmy, in 1983, 1986, 1993. He won the Sir Laurence Olivier Award for Mephistopheles in Busoni's Doktor Faust, English National Opera in 1986.

He was awarded an Honorary Doctor of Letters, Loughborough University, in 1999; the Sir Reginald Goodall Award, The Wagner Society, London, in 2001; the Sherwin Award, The Wagner Society of Southern California, Los Angeles, in 2009; and an Honorary Bachelor of Science, Loughborough University, Centenary Honorary Degree, in 2009.