Making his name as a hard bop player, he appeared regularly at the Marquee Club from August 1960, 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. He spent most of 1962 in Calcutta, India as part of the Ashley Kozak Quartet, playing three 2-hour sessions seven days a week, before returning to the UK and forming his quartet with Harry South – who had also been in the quartet in Calcutta – on piano. They were joined by former The Jazz Couriers bassist Phil Bates and variously, another ex-The Jazz Couriers member, Bill Eyden, Jackie Dougan or Phil Seamen on drums. The Dick Morrissey Quartet recorded three LPs, "Have You Heard?" (1963); the live recording "Storm Warning!" (1965) on Mercury; and "Here and Now and Sounding Good!" (1966). The quartet, played regular London gigs at The Bull's Head, Barnes and at Ronnie Scott's, whose manager, Pete King, once said that Ronnie's was kept going in those days due to the crowds Dick Morrissey pulled in. 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.