Charles was speaking on Michael Berkeley's Private Passions in a special episode recorded in the Garden Room at Clarence House, which aired on BBC Sounds on Boxing Day.
The royal spoke at length about the role of music in his life in the long-running Radio 3 programme, in which famous guests discuss "their musical loves and hates".
Speaking about Camilla's "terribly romantic" 2007 birthday surprise, Charles recalled: "[It was] entirely at the suggestion of the Philharmonia, of which I've been a very proud patron for nearly 40 years."
And paying tribute to conductor Christopher Warren Green, he added: "He was terribly keen I should conduct it. I said: you must be out of your mind.
"Finally he persuaded me against my better judgment and we did it as a special surprise."
Charles also paid homage to his late grandmother, the Queen Mother, who reportedly loved 'Sadie the Shaker' the 1930s classic by Syd Lipton & Grosvenor House.