Born in Nelson, New Zealand in 1932, Begg studied in Auckland with Sister Mary Leo and at the New South Wales State Conservatorium, during which time she won the 1955 Sydney Sun Aria contest. She was engaged as a principal mezzo-soprano with the National Opera of Australia from 1954–56. Her professional debut was as Azucena in Verdi's Il trovatore. She went to London in 1957 to attend the UK's National School of Opera on a musical scholarship. Between 1959–62 she appeared with the Carl Rosa Opera Company, the New Opera Company, the Royal Opera and the English Opera Group in a wide variety of roles. In 1959 she took part in the New Zealand Music Society's concert at the Wigmore Hall, with a performance of Hindemith's The Four Temperaments; the following year Sadler's Wells offered her the part of "Goddess Juno" in Offenbach's Orpheus in the Underworld, where she discovered she had a talent for comic opera. She returned to New Zealand in 1964 to sing with the New Zealand Opera Company until 1966, but still made guest appearances at Bordeaux, Chicago and elsewhere. She was named the principal resident mezzo-soprano at the Royal Opera, Covent Garden, where she stayed for 10 years. Her roles there included Flora in La traviata, Mary in The Flying Dutchman, Emilia in Otello, Mamma Lucia in Cavalleria rusticana, Madame Larina in Eugene Onegin, the Grandmother in Jenůfa, Marthe in Faust, Mrs Sedley in Peter Grimes, Teresa in La sonnambula, Anna in Les Troyens, and Marina Mnishek in Boris Godunov. In 1975 she appeared as Marcellina in the Chicago Lyric Opera's production of The Marriage of Figaro, which led to her reprising the role in Jean-Pierre Ponnelle's film of the work, where she appeared alongside Mirella Freni as Susanna and Hermann Prey as Figaro. She also appeared in Gilbert and Sullivan for the D'Oyly Carte Company, and she appeared in such roles at the BBC Proms.She also appeared as Katisha in The Mikado at The Sydney Opera House with The Australian Opera, a definitive performance of the character, and it was issued on video. She had then accepted an invitation from Richard Bonynge to join the Australian Opera, where she remained for the rest of her career. Here she took on major roles such as Carmen and Amneris, and appeared in Boris Godunov and The Mastersingers of Nuremberg. Her final appearance was at the Sydney Opera House in 2006 to recreate Grandmother Buryjovka in Jenůfa, conducted by Richard Hickox.
Marriage
She married Johnnie King, a Canadian, in 1964. He died in 1979. They had no children.