Davis was for more than a decade both the chief conductor of the BBC Symphony Orchestra and the musical director of Glyndebourne festival opera.
Between 1988 and 2018 he led proceedings at the Last Night of the Proms on 12 occasions, twice delivering the customary conductor speech in the manner of the major-general in Gilbert and Sullivan's The Pirates of Penzance: "This is the very model of a modern music festival."
His agent, Jonathan Brill, told the PA Media news agency that he had been diagnosed with leukaemia, which became acute shortly after his 80th birthday on 2 February.
Among those to pay tribute yesterday was the mezzo-soprano Dame Sarah Connolly, who said she was terribly saddened at the news.
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