This is Julie Andrews as a guest on The Dick Cavett Show in 1971. The fellow to her right is her husband, writer-director Blake Edwards. And Cavett asks her to sing "Wouldn't It Be Loverly," which she does with remarkable ease and the purest of voices, an utterly graceful performance just sitting comfortably in her chair. (And happily done in Eliza Doolittle-character with the Cockney accent.)
Note: afterwards, they joke about plaid pants and Cavett talks about seeing My Fair Lady in the wings. That's all a reference to the first part of the interview when he tells a story about when he was a Yale student seeing the opening night tryout performance of My Fair Lady in New Haven and afterwards going backstage.