Digby was born in 1932 at Jabalpur in Madhya Pradesh, and was the grandson of William Digby, a member of the Indian Civil Service who, in the late 19th century, wrote extensively about the poverty created by British rule in India. His father was Kenelm George Digby, a judge of the Indian High Court, and his mother was Violet M. Kidd, an accomplished painter. As his father was a friend of J. F. Roxburgh, the first headmaster of Stowe School, Digby was sent to that school after attending a preparatory school in North Wales. In 1951 he went with his mother on a painting expedition to Delhi, Rajasthan and Kashmir. On his return to Britain he attended Trinity College, Cambridge, where, in 1954, he obtained first-class honours with distinction in History.

Digby knew how to read Urdu and Hindi, and while at the University of Cambridge he attended classes in Persian and began to publish his own translations of Persian poems. He lived in Whewell’s Court and it was here that he welcomed Amartya Sen when he arrived in Cambridge in the summer of 1954. In 1957 he returned to India for two years sponsored by a grant from the Worshipful Company of Goldsmiths. During this time he learned about Indian art history and museology. In 1959 he travelled to Pakistan, where he visited Lahore, Rawalpindi, Balakot, the Kaghan Valley and Peshawur, among other places. On his return to London Digby lived in a tiny house in Camberwell while he studied at the School of Oriental and African Studies where he focused on the Sultanate period.

In 1962 he returned to India where he spent almost a year in Hyderabad and another year in Delhi during which period he wrote on Indian history and contributed an article on the Emperor Humayun to the Encyclopaedia of Islam. This was his first article for this work. He also contributed to the first volume of The Cambridge Economic History of India. His first major article was Dreams and Reminiscences of Dattu Sarvani, a Sixteenth Century Indo-Afghan Soldier, which sprang from Digby's interest in medieval Indian warfare and Indian Sufism. On his return to London he became a regular reviewer in The Journal of the Royal Asiatic Society, the Bulletin of the School of Oriental and African Studies and The Times Literary Supplement. From 1969 to 1985 he was the Honorary Librarian of the Royal Asiatic Society, which involved him in ordering and cataloguing the Society's collections.

In 1971 Digby hitch-hiked to Venice with his friend Richard Harris, who later was the BBC World Service’s regional manager in Delhi. The two left Venice and travelled by sea to Rhodes and Anatolia, and then on public transport through Turkey to Tehran, Kirman, Zahidan and Quetta. Digby was in Karachi when war broke out between India and Pakistan, and here he privately published his book War-Horse and Elephant in the Dehli Sultanate. In 1972 he was appointed Assistant Keeper in the Department of Eastern Art of the Ashmolean Museum in Oxford. This was to be his only full-time paid position, he having benefitted from a number of legacies from deceased relatives. At the Ashmolean, and on a tight budget, he made a series of purchases of Indian decorative arts that were exceptional for their quality.

As an ex-officio member of the Oriental Faculty of the University of Oxford, Digby was responsible for supervising postgraduate students, and gave instruction in Hindi, Urdu and Persian. In addition, he examined postgraduate theses including that of Michael Nazir-Ali. Digby also served as visiting professor in Paris and Naples, where he lectured on Sufism and architecture. In 1999 Digby was awarded the Burton Medal of the Royal Asiatic Society and delivered a paper later published as Richard Burton: the Indian Making of an Arabist. In his latter years Digby lived in a cottage in Jersey which had been left to him by a relative. From here he made annual visits to India.

Simon Digby died of pancreatic cancer in Delhi on January 10, 2010, having been diagnosed with the disease only on December 28, 2009. He was cremated in India on January 14, 2010 and his ashes immersed in flowing water. Digby was unmarried and left no close relatives.