This is all I can find in Wikipedia about that:
"Although details of Morse's career are deliberately kept vague, it is hinted that he won a scholarship to study at St John's College, Oxford. He lost the scholarship as the result of poor academic performance resulting from a failed love affair, which is mentioned in the series in Season 3, Episode 2, "The Last Enemy", and recounted in detail in the novel The Riddle of the Third Mile, chapter 7. Forced to leave the University, he entered the Army and, on leaving it, joined the police. He often reflects on such renowned scholars as A. E. Housman who, like himself, failed to get an academic degree from Oxford."