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She also met the broadcaster's Director General on the visit to the BBC's Burmese Service, part of her four-day visit to Britain.
During the visit, Ms Suu Kyi briefly met Dave - known as the "Hairy Cornflake" - whose show she tuned into during 15 years spent at her parents' house in Rangoon.
The Nobel laureate has previously told how the BBC World Service request programme A Jolly Good Show - presented by the DJ for 20 years - was a lifeline during her time in confinement, saying it made her world "much more complete".
Dave told her: "It's just such a pleasure to meet you in person after all the nice things you said about the programme."
She replied that she was "thrilled" to have heard the voice of a Burmese boy on the show.
"Well that's the World Service," Dave answered. "It does what it says on the tin, and I am just glad to have been a part of the things that you listened to that helped you."
The DJ, who now has a show on Magic radio network, kissed Ms Suu Kyi on the hand, adding: "It's a real privilege to meet you."