Expect to feel possessive about Patmos. Within 24 hours of stepping ashore for your first visit, the island’s beauty and serenity will seep into your psyche, and you’ll find yourself breathing a quiet sigh of relief once the last boatload of day-trippers has left. Soon you’ll begin to begrudge their presence entirely. Then you’ll get home and start spouting gibberish, like “Lovely island, shame about the leprosy”, just to deter people from going there. In short, Patmos is the kind of place you will want to keep firmly under your sunhat.

Mythology and history tug at this Dodecanese island as insistently as the cobalt waters of the Aegean. Patmos has been an outpost for exiles, including Orestes, on the run from the Furies for matricide, and Yacub, the evil black wizard who created the white race there (according to the Nation of Islam). Its most famous outcast was St John the Evangelist: having been exiled from Ephesus in AD95, he is credited by posterity with authoring a Gospel and the Book of Revelation here, both written in a tiny hillside cave.

The medieval monastery of St John, begun in 1088, dominates the island both visually and politically. Its status has brought prosperity and a deep sense of place, while its religious influence has put the brakes on the kind of holiday hedonism that is cheapening many of its island neighbours.

This is not to say that life here is po-faced. You can’t fault the friendliness of the people, at least not until fatigue sets in during August peak season. The main settlement and port, Skala, right in the middle of the butterfly-shaped island, is a lively evening out. But refreshingly, nobody goes out of their way with the hard sell — probably because they don’t have to. The island speaks for itself.

Hora and the monasteries: the Monastery of St John is a must-see — built like a castle to repel pirates and marauders from Asia Minor. The inner narthex contains a striking icon of St John holding his Gospel (imitated in souvenir shops all over the island); while the Chapel of the Panayia has some impressive medieval frescoes, including Christ depicted as a young Byzantine emperor.

The monastery’s museum (£4), too, is worthwhile. Its 13th- and 14th-century icons, from the Cretan school, hint at a transition from a linear Byzantine style to a more painterly approach, presaging the Renaissance.

The Monastery of the Apocalypse nestles halfway down the hill towards Skala, built around the cave in which John received his visions of the end of the world. Tag along with one of the tour groups to hear a suitably dramatic account of how God spoke through a great fissure traversing the roof, which splits into three at the cave mouth in an echo of the Trinity.

Getting lost, and found again, in the mazy hilltop settlement of Hora is a joy — its dazzling whitewashed houses, many refurbished as holiday homes by wealthy Greeks and foreigners, lend it a Cycladic feel, and a rather dutiful stillness blankets the town by day and night. See if you can find lovely Platia Vangelis, the hub of Horan nightlife, with its friendly family-run restaurant.

Beachcombing: Patmos’s beaches all share limpid waters, but each has a distinct identity, and you are likely to develop a personal favourite. The beach at Livadhi Yeranou, with an islet to swim to, good snorkelling and a delightful taverna serving sea urchin (a local delicacy), became mine.

Bored with sun-worshipping? Scramble around Kalikatsou Rock at the end of Grikos beach — at your own risk, of course — which contains caves hollowed out by Christian hermits.

The island’s sole sandy beach is at Psili Ammos, in the far south. Hop on one of the ferries from Skala, which leave at about 10am. The beach is well worth the trip, with plenty of shady tamarisks and a very basic taverna that serves goat. In high season, you may have to fight for space with naked German volleyball players — discreet naturism is a part of beach culture here.

There are also countless hidden coves all over the island, so if you’re intrepid you may well find your own secret beach.

Watersports: Kambos beach is the watersports hub of Patmos, and throngs with young Greeks competing for tanning space. Activities are co-ordinated by the friendly Andreas — if he looks familiar, it's because you've seen him DJing in the Konsolato Music Club, one of Skala's late-night hang-outs. A 15-minute wakeboarding or water-skiing session costs £17, and windsurfing will set you back £14 an hour. Despite a recent relaxation of diving restrictions, there is as yet nowhere to dive on Patmos, although this may change soon.

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