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Shaw played regularly both live and as a session musician for many British jazz musicians over the course of the next twenty or so years, working with Joe Harriott, Tony Crombie, Don Rendell, Tony Kinsey, Stan Tracey, Bill Le Sage, and others.
Soon after playing with Reinhardt, he played in a Count Basie ensemble which also included Malcolm Mitchell and Tony Crombie; he played with both of them after leaving Basie, working together with Hoagy Carmichael and Maxine Sullivan and touring in Sweden together with Reinhardt and Stéphane Grappelli.
In 1954, he was in the Tony Crombie Orchestra, together with Dizzy Reece, Les Condon (trumpet), Joe Temperley, Sammy Walker (tenor saxs), Lennie Dawes (baritone sax), and Ashley Kozak (bass).