His grandchildren include Grammy Award winning classical music producer James Mallinson, actor David Mallinson and actress Phoebe Nicholls and his great-grandchildren are actors Tom Sturridge and Matilda Sturridge.
He has won a total of 15 such awards in his career, his most recent Grammy nominations - and wins - having come in 2008 for Best Opera Recording.
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He made only one full-length recording, for Decca Headline, "Salman Shukur - oud", HEAD 16 PSI, recorded in Rosslyn Hill Chapel in London in 1976 by James Mallinson and Stanley Gooddall, notes by John Haywood, released in 1977, and a brief excerpt of his solo oud performance in Rast Iraq can be heard on the Tangent Record series Music In The World Of Islam: Lutes (re-issued by Topic Records).