The Any Questions? presenter also confessed that he took cannabis on two separate occasions.
Speaking to The Daily Telegraph, he said: "I had cannabis twice in my early 20s. And once, in America, at around the same age, I did a line of cocaine.
"I sneezed it all over the place much to the dismay of the people around who saw it as this precious substance. It tickled my nose, and then it blocked my nose. And I had no experience from it at all."
Jonathan - the brother of Question Time moderator David - added in the interview: "Maybe if I had a tremendous buzz or a high or whatever the experience is supposed to be, I would have done it again. But I didn't, and I haven't."
A South American Journey with Jonathan Dimbleby continues this Sunday at 9pm on BBC One.