This is the only surviving recording of Virginia Woolf's voice. It is part of a BBC radio broadcast from April 29th, 1937. The talk was called "Craftsmanship" and was part of a series entitled "Words Fail Me".
The audio is accompanied by a slideshow of photographs of Virginia Woolf.
The text was published as an essay in "The Death of the Moth and Other Essays" (1942)
I came upon this recording of Virginia Woolf speaking about writing just as I was about to start reading Mrs. Dalloway for the first time. It's a bit mesmerizing to hear her.