Garrick was born in Enfield, Middlesex,[2] and educated at University College, London, from which he graduated in 1959 with a BA in English literature.
Soon after graduating, Garrick became the musical director of "Poetry & Jazz in Concert", a roadshow devised by poet and publisher Jeremy Robson, and involving writers as diverse as Laurie Lee, Adrian Mitchell, Vernon Scannell, Spike Milligan, Dannie Abse, and John Smith.
[3] Garrick came to special prominence in the British contemporary jazz world initially as the pianist with the Don Rendell–Ian Carr quintet from 1965 to 1969, and led his own sextet from 1966.
Jazz Praises, an extended religious work for his sextet and a large choir, was performed at St. Paul's Cathedral in London, and elsewhere.
That year, he also participated in the release of a 1964 recording, The Girl with Brown Hair, featuring his trio (with Colin Barnes on drums and Dave Green on bass) backing Dick Morrissey.