Alice McVeigh was born in South Korea, of American diplomatic parents, and lived in Southeast Asia until she was 13, when the family returned to the suburbs of Washington D.C. She then began to play the cello, winning, among others, the Beethoven Society of Washington cello competition, as well as being selected as a finalist in the National Music Teachers Association Young Soloists competition and the National Symphony of Washington Young Concert Artists award.

She achieved a B.Mus with distinction in performance at Indiana University School of Music in 1980, the same year in which she came to London to study privately with William Pleeth. Since then she has freelanced with orchestras including the BBC Symphony Orchestra, the Royal Philharmonic and Sir John Eliot Gardiner's Orchestre Révolutionnaire et Romantique all over the UK, the EU, America and the Far East.

In the 1990s Alice's two novels, based on the secret life of an orchestra, were published by Orion and her first play was put on at the Lewisham Theatre (Beating Time).

Alice has been married to Simon McVeigh (currently deputy Vice-Chancellor at Goldsmiths College, University of London) since 1981: their only child Rachel recently played principal French horn in the National Children's Orchestra.