In 1737 a work was published in London, Memoirs of Sgr. Gaudentio di Lucca (in later editions it was sometimes published as The Adventures of Sgr. Gaudentio di Lucca). It was a runaway bestseller; it would be reprinted many times and translated into many languages. Since it was published in the eighteenth century when subtitles do the work of blurbs, you can get some idea of the substance of the work from its subtitle (the humor of its length is probably deliberate): taken from his confession and examination before the fathers of the Inquisition at Bologna in Italy. Making a discovery of an unknown country in the midst of the vast deserts of Africa, as ancient, populous, and civilized, as the Chinese ... Copied from the original manuscript kept in St. Mark's library at Venice; with critical notes of the learned Signor Rhedi, late library-keeper of the said library. To which is prefix'd, a letter of the secretary of the Inquisition, to the same Signor Rhedi, giving an account of the manner and causes of his being seized. Faithfully translated from the Italian by E. T. Gent.. It is a work of fiction originally written in English, and telegraphs that fact fairly clearly. It's quite a good book, relatively fast-moving and surprisingly funny, using intricate layers of narration in a highly effective way despite not being all that long; it's not surprising that it became so popular. Historically, it's of significance in part for being a major part of the transition between Utopia novels and Lost World/Dark Continent adventure stories, a precursor of H. Rider Haggard, and one of the works that, because of its popularity, established some of the genre conventions and possibilities for it.
As the work was published pseudonymously, speculation about its author sprang up immediately, and one name seems to have spread most widely: George Berkeley, the philosopher and Bishop of Cloyne. For most of the late eighteenth century most people regarded it as Berkeley's work. I first came across the name of the novel when reading Sir William Forbes's An Account of the Life and Writing of James Beattie; in a letter to the Duchess of Gordon in 1780, Beattie mentions (toward the end) that he is sending her a parcel of books, one of which is Gaudentio; he praises the description of the African deserts, and says, "The author is no less a person than the famous Bishop Berkeley."
Alas, the work is almost certainly not by Berkeley. Indeed, it's difficult to say why it would have been attributed to Berkeley in the first place. It likely lies in a complex set of associations. The humor is (very) broadly of the sort that would have been associated with Jonathan Swift -- Gulliver's Travels had been published a few years before it, and is probably an influence, although Gaudentio is much subtler and strives to be more realistic than Gulliver (not that that is difficult). The earliest attribution I've been able to trace was a review in Gentleman's Magazine not long after it came out; it's vague, but the sense of it seems to be that the reviewer thought that it was by Swift. However, at some point it became associated with Berkeley. And it is true that if you assume that the work originated in Swift's circle, Berkeley is actually the best candidate, particularly give the relative popularity of Alciphron. He was a close friend of Swift and all his circle, and we know from some of his essays and occasional touches in his published works, especially Alciphron, that he is capable of writing broadly Swiftian humor; Berkeley was a Platonist, so might be thought attracted to the idea of writing a Utopia (this was explicitly given as a reason for attributing the work to him in at least one case); he had considerable erudition, including some knowledge of the Ancient Egyptians, which plays a role here; and perhaps more obviously, Gaudentio has a satirical portrait of a freethinker that would likely remind people of the satirical portrait of freethinkers in Alciphron. In addition, Berkeley was known to have traveled in Europe, particularly Italy, and he was famous for his idealistic plan for a school in Bermuda, giving him an association with exotic travel, even though he never visited Africa or even made it to Bermuda. And it has to be admitted that Berkeley has the writing ability for it; he has a knack for description of scenery and can easily blend philosophical and narrative elements.
On the opposing side, however, is the fact that Berkeley's son denied that Berkeley wrote it, or even read it, and if you don't assume that it originated in Swift's circle, there's not much reason to attribute it to Berkeley. It was hardly the first Utopian novel; it was a genre that sold very well at the time. The humor is perhaps harsher and, occasionally, edges up to risqué (an occasional joke is that the narrator pretends that pages got lost right at the moment the narrative gets into discussion of some sexual topic) a bit more than you might expect of Berkeley beforehand. If there's any connection between the satire on freethinkers in Alciphron and the satire on them in Gaudentio, the former had been published in 1735, so it could easily have been an influence on the latter in just the ordinary way. The question was investigated quite well in Notes and Queries, and the argument against Berkeley's authorship seems fairly probable. After the Berkeley attribution began to collapse, people looked around for whomever could be a possible alternative candidate. One suggestion, derived from a later close investigation published in Notes and Queries, was a certain Simon Berington, about whom we know relatively little, but who was probably a Catholic priest, and certainly from an old Catholic family. Later investigation did seem to show that it was a local family tradition that Berington had written the work. And if we compare Gaudentio to other things we're fairly sure Berington wrote, such as A Popish Pagan, a biting and thorough satire of the controversial work of Conyers Middleton, or the work that James Crossley, the second Notes and Queries researcher, used, Dissertations on the Mosaical Creation, there does seem to be some at least broad kinship of humor ideas between the works, and Crossley points out that when one compares the authors quoted or alluded to in the works, there is a fair amount of overlap. It does seem fairly certain, then.
In any case, if you've never read it, it is worth reading, and it is a book that is good enough that it probably should not be allowed to fall into oblivion. As I mentioned before, for a Utopia novel, it is fast-paced, in an H. Rider Haggard sort of way. There is a lot of humor in the work, ranging from the subtle to the blatantly sarcastic. And Berington's use of narrative layering borders on genius -- reading the story, we are reading a supposed translation and edition of a supposed commentary by an Italian scholar of an account by Gaudentio of his adventures, including stories told to him by natives, as recorded in the transcript of an Inquisition investigation, and each layer gets some good use in the story. We travel with Gaudentio to Egypt, where he meets a man called the Pophar, who takes him to his homeland, the forgotten but mighty, wise, and prosperous civilization of Mezzorania, deep in the heart of Africa, and its glorious capital city of Phor, also called No-om or No-Ammon, in which the long-lost civilization of the Ancient Egyptians has had its greatest flowering.
A. D. Harvey and Jean-Michel Racault have an interesting article discussing the work in its literary context (PDF).