Jenny Abramsky, BBC Director of Audio and Music, said he had been "one of the wonders of radio broadcasting for years".
Jazz trumpeter Digby Fairweather said that Lyttelton "was, in the best possible way, a jazz machine".
"We will probably never have another Humphrey Lyttelton, which is terribly sad really," he added.
"But we can always play his records."
You can hear a classic edition of I'm Sorry I Haven't a Clue on BBC Radio 4 on Sunday 27 April at 1200 BST. There will also be a special programme in tribute to Humphrey Lyttleton on Wednesday 30 April at 0900 BST.
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