After studies at Peterhouse, Cambridge, he became a teacher. He joined the Foreign Office in 1939. His diplomatic career culminated with his posting to Prague, where he was the British Ambassador from 1960 to 1966. On retiring from the Foreign Office, he became first Professor of Russian and Soviet Studies and later Professor of Central and South-Eastern European Studies and Director of the Comenius Centre at the University of Lancaster.
Parrott is best known for his translation of Jaroslav Hašek's The Good Soldier Švejk. He also translated some of Hašek’s short stories, The Red Commissar. He also wrote a study of Haseks short stories 
- Hašek, Jaroslav (1981), The red commissar : including further adventures of the good soldier Švejk and other stories, W. Heinemann, ISBN 978-0-434-31376-1
- Parrott, Cecil Sir (1982), Jaroslav Hašek : a study of Švejk and the short stories, Cambridge University Press, ISBN 978-0-521-24352-0
- Parrott, Cecil Sir (1975), The tightrope, Faber and Faber, ISBN 978-0-571-10256-3
- Parrott, Cecil Sir (1977), The serpent and the nightingale, Faber, ISBN 978-0-571-10869-5
- Parrott, Cecil Sir (1978), The bad Bohemian : the life of Jaroslav Hašek, creator of The good soldier Švejk, Bodley Head, ISBN 978-0-370-10344-0
- Parrott, Cecil Sir (1983), The bad Bohemian : a life of Jaroslav Hašek creator of the good soldier Švejk, Abacus, ISBN 978-0-349-12698-2