[3] Self-taught, he started playing clarinet in his school band, The Delta City Jazzmen, at the age of sixteen with fellow pupils Robin Mayhew (trumpet), Eric Archer (trombone), Steve Pennells (banjo), Glyn Greenfield (drums), and young brother Chris on tea-chest bass.

Going on to join trumpeter Gus Galbraith's Septet, where alto-sax player Peter King introduced him to Charlie Parker's recordings, he began specialising on tenor saxophone shortly after.

[4] Making his name as a hard bop player,[5] he appeared regularly at the Marquee Club from August 1960,[6] and recorded his first solo album at the age of 21, It’s Morrissey, Man!

(1961) for Fontana, featuring Stan Jones on piano, Colin Barnes on drums, and The Jazz Couriers founding member Malcolm Cecil on bass.

During this time he also played extensively in bands led by Ian Hamer and Harry South, including The Six Sounds, featuring Ken Wray and Dick Morrissey, a band which by 1966 had developed into the Ian Hamer Sextet featuring South, Dick Morrissey, Keith Christie, Kenny Napper and Bill Eyden, among other leading UK-based jazz musicians.

Likewise, together with fellow tenors Stan Robinson and Al Gay, baritone sax Paul Carroll, and trumpets Ian Carr, Kenny Wheeler and Greg Brown, Dick Morrissey formed part of (Eric Burdon and) The Animals' Big Band that made its one-and-only public appearance at the 5th Annual British Jazz & Blues Festival in Richmond (1965).

During their stay in New York, word got around, and soon big names began arriving to join them for jam sessions, such as Steve Gadd, David Sanborn, George Benson and, every night for a week, the Brecker Brothers.

Apart from the early recordings with visiting US performers mentioned above, Dick Morrissey also toured and/or recorded with Charly Antolini, Alexis Korner (several albums), Hoagy Carmichael, participating on Hoagy's last album, In Hoagland (1981) featuring Georgie Fame and Annie Ross, with arrangements by Harry South, Mike Carr, Georgie Fame, Brian Auger, Dusty Springfield, Freddie Mack, Pete York, Paul McCartney, Orange Juice, Gary Numan (he appeared on a number of Numan's albums throughout the 1980s), Phil Carmen, Herbie Mann, Shakatak, Peter Gabriel (the solo in "Start" and several other tracks from his third album), Jon Anderson (and as a member of the New Life Band's The Song of Seven Tour in 1980), Demis Roussos, Jon & Vangelis and Vangelis, Gino Vanelli, as well as playing the haunting saxophone solo on the Vangelis composition "Love Theme" for the 1982 film Blade Runner.

Other musicians and performers Dick Morrissey shared the stage with include Allan Holdsworth, Robert Fripp, David "Fathead" Newman, Tommy Körberg, Boz Scaggs, Johnny Griffin, David Sanborn, Steve Gadd, Richard Tee, Billy Cobham, Michael Brecker, Randy Brecker, Sonny Fortune, Sonny Sharrock and Teddy Edwards (with whom he jammed a "duel" at London's 100 Club in the early 1980s), Mel Collins, Dick Heckstall-Smith, John Surman, Graham Bond, Klaus Doldinger, Al Casey, Miller Anderson, Bridget St. John, Paul Carrack, The Style Council, Daryl Hall, Keith Emerson, Shakatak and so on.

Ronald Atkins, writing in The Guardian, put it thus: "John Coltrane's approach to the tenor had yet to make much of an impact in Britain, and Morrissey came up with a startling and warmly appreciated blend of Stan Getz and Sonny Rollins, the phrasing of one allied to the abrasive tones of the other.

His command of the tenor saxophone was masterly, but it was the unforced fluency of his playing, expressed in a characteristically broad and sweeping tone, that attracted the greatest admiration.