A con man is only as good as his charm. Frank William Abagnale, reincarnated by Leonardo DiCaprio in “Catch Me if You Can,” inhabited half a dozen identities by the time he was 21 and did so with such brio that he was able to fool hundreds. Charles Ponzi was a dapper operator who tooled around in a Locomobile. And Ronnie Cornwell, the father of the novelist John le Carré, was an insurance fraudster who later became the model for the charismatic Rick Pym in le Carré’s “A Perfect Spy.” The most famous image of Cornwell shows him in a top hat and buttonhole striding confidently through a top-class English crowd, with a look of knowing concentration mixed with an offhand breeziness. You can feel the charm coming off the image.

In Adam Sisman’s amusing and elegantly written biography of the midcentury British impostor Robert Parkin Peters, excitedly styled “Peters the Parson” and “Romeo of the Church” by the yellow press, the subject is a curious and relatively harmless man of many faces who managed to attract the attention of one of Britain’s most august modern historians. The suavely aristocratic and yet strangely gullible Hugh Trevor-Roper first encountered Peters at Oxford in 1958 when Trevor-Roper, then a Regius professor of modern history, received a letter from an unknown supplicant on behalf of a Mr. and Mrs. Peters. They were young academics suffering “vindictive persecution from outside the university.” Could the professor help?

Trevor-Roper was curious. Having made his name in 1947 with “The Last Days of Hitler,” which drew on his wartime work with MI6, he was, at 44, one of the most famous men at Oxford and indeed in the country. He offered his assistance to Peters and eventually agreed to meet him. “Peters,” Sisman writes, “was a small, chubby-cheeked, bespectacled man with thinning hair and an earnest manner, who spoke with a slight lisp.” He was a graduate student in divinity at the prestigious Magdalen College, which had for some reason neglected to go through his application materials with their customary diligence.

Although Trevor-Roper did not know it at the time, Peters had been born with a skeletal deformity that had forced him into a metal frame during his formative years. He claimed to be 34 but was most likely 40. Pugnacious, yearning to be a genuine theological academic, Peters struck the historian as curiously impressive in some way. He said he had been persecuted by the bishop of Oxford “in the most unaccountable manner,” barred from officiating for reasons unknown. Intrigued, Trevor-Roper agreed to look into the matter — and by doing so opened a door into the parallel life of Robert Peters, bigamist extraordinaire, false priest, phony academic and, for a time, a respected member of Magdalen College. Not to mention erstwhile husband to at least seven women, none of whom suspected that he was not an upright man of religion.