I'm glad you asked that question. They are (or were), of course, off the south coast of Cornwall, and may or may not be identical with the land of Lyonesse, located in the same vicinity, and attested in several sober medieval chronicles, in spite of what modern maps will tell you. It is theorized that, like Lyonesse (if in fact the two were not identical) they sank into the sea in 1601, thus opening the way for The Age of Exploration. Little else is known for certainty of its geography, except that it extended to latitudes where rattan flourished. And that parts of it were bloody hot in the summer.
Its proximity to Europe is testified to by its typical European social institutions, with Kings, Dukes, Baronies, Shires, the Order of Knighthood, etc. It is supposed that it was populated entirely by people lost on their way to someplace else, which explains the genetic inability of its inhabitants to write decent event directions. That would also explain two missing features of this otherwise rich culture: the almost complete absence of both the Christian church and the lower classes. It is likely that all the priests and the servants were on another, different ship that reached its intended destination safely.
There is further evidence that it is, or was, located in the vicinity of the British Isles: the unusually high proportion of Celts with unpronounceable names in the population (explained by the obvious closeness to Celtic territories) and the language. In spite of national origin, most inhabitants spoke English, whether they themselves were French, German, or Berber. Presumably, a boatload of English got to the place first, voted in English as the Official Language, and enforced it on everyone that showed up later.
The fact that most of the inhabitants were not native speakers of English, has, however, left its mark on the tongue of the Laurel Kingdoms. Loan words and usages unknown to medieval English crept into the dialect: "dragon" instead of "car", "small" instead of "child" "feastocrat" instead of "head cook". Not to mention a tendency to pronounce chirurgeon as "ki-rur-ge-on" rather than the more typical medieval pronunciation as "surgeon"
There are two theories about relations between the Laurel Kingdoms and the Far East. Some maintain that in fact, significant numbers of Japanese, almost all of them Samurai Warriors and Ninjas, visited the place en route to Europe before 1601. (According to the theory this is not inconsistent with the fact that documented Japanese visitors to pre-17th c. Europe were somewhat less common than Anti-Popes, since only the small number of Japanese that failed to bump into the Laurel Kingdoms got through to Europe proper.)
The alternative theory is that Sir Francis Drake picked up a shipload of surplus kabutos, do-marus, katanas, and ninja stalking suits in an otherwise undocumented visit to Japan, and visited the Laurel Kingdoms on his way home to Kent. Proponents of this theory point to the otherwise improbable number of blond, blue-eyed people wearing this equipment, and suggest persuasively that If That Was a Real Ninja You Wouldn't See Him Now, Would You?