He wrote a number of books on Islam and its history, and from 1938 to 1946 was Professor of Arabic at the School of Oriental and African Studies.

His father was the senior pastor of a Congregational church in Great Yarmouth, but when Tritton was still young the family moved to Wandsworth.

He taught at the Friends' Mission School in Brummana in Lebanon, and then at the universities of Edinburgh and Glasgow.

In 1921, he was appointed Professor of Arabic at Aligarh University in India, where he remained for the rest of the decade.

Two years later, he was promoted to Reader, and in 1938 he succeeded H. A. R. Gibb as Professor of Arabic and Head of Department.