With a guttural command and a flick of the whip, Dimitri spurred his horses into first gear. I’ve been driving a fayton since I was 14 years old,” he says, “but I’ve never in my life learned to drive a car.”

Since Dimitri has lived all his 65 years on Büyükada, an island in the Sea of Marmara, this was hardly surprising. Apart from two police cars, an ambulance and a fire engine, there are no vehicles on Büyükada whatsoever, and the only form of public transport is by fayton (horse-drawn carriages) like the one that Dimitri handles so smoothly.”

The cobbled streets of the Old Town are lined with the racks of bicycles that provide the transport for a population that increases dramatically during the summer holidays. They say that in July and August, you might be more in danger here from whizzing bicycles than you would ever be from the trams and buses that tear along the Istanbul waterfront. But the roar of engines and the constant honking of horns are replaced here by the clatter of hooves and the occasional braying of a donkey. In the peaceful, tree-lined avenues of Büyükada you quickly forget that you are only an hour-and-a-half by ferry from the bustle and clamour of Istanbul.

It is estimated that as many as 20 million people now live in Istanbul. As one of the world’s fastest growing cities spreads its skirts up the European and Asian shores of the Bosphorus and down along the coasts of the Sea of Marmara, the elite have been irresistibly drawn to this haven of tranquillity. Many came here to build the wonderful wooden yali summer houses and mansions that line the streets of Büyükada town.

Trotsky’s house,” said Dimitri, as we trotted past a particularly austere looking building. Its facade was carved into a sort of scrolled lacework and its shutters were battened tight against the Turkish sun, just as it might have been when the famous exile was in residence.

Leon Trotsky lived on Büyükada from 1929 to 1933 after he was ousted from Stalin’s Russia. Despite spending most of his time behind locked doors and under the vigilance of armed guards, Trotsky was obviously very fond of the island, which he described as “an island of peace and forgetfulness”.

The great revolutionary was the last in a long chain of exiles in the archipelago that is known as the Princes Islands.

Throughout history, members of the Constantinople nobility who had fallen from grace were sent here – usually by their own family who, with shocking thoroughness, had them blinded first. The first Byzantine Empress came to power only after plucking out the eyes of her son and exiling him to Büyükada. A contemporary wrote that “the sun put away his rays in horror at this unnatural act, and the sky was darkened for 17 days”. Justice was swift, however, and Empress Eirene ruled for only five years before she in turn was consigned to the islands.

It is said that the exiles were often driven half crazy by the scent of jasmine, honeysuckle and mimosa that pervades these islands and by the thought that the marvels of Constantinople, so accessible to others, would forever be beyond their sight. To the natives of the islands, life here has always been blessed: fruit and flowers, that are scarce on the mainland, grow in abundance here and the rows of wonderful fish restaurants along the waterfront testify to the legendary riches of the Sea of Marmara.

On an island that is only two-and-a-half miles long, everywhere is easily accessible, but Dimitri’s fayton was taking me on the first leg of a journey that was perhaps as timeless as the island itself. At the bottom of Yüce Tepe hill, highest in the archipelago, Dimitri eased his two bays to a halt and I climbed down to start the trek up the cobbled trail to the Monastery of St George Koudonas. The walk is not particularly hard but, for the sake of authenticity, many visitors hire donkeys from this point so that they can arrive at the monastery in true ‘pilgrim style’.

Devotees have come here to pay homage for over a thousand years. Traditionally those on foot can make a wish if they do the climb barefoot, and the bushes are festooned with knotted white and red ribbons and bits of paper, each representing a prayer. Inside the monastery other offerings have been made, not only by Greek Orthodox worshippers, but clearly by people of every denomination. Visitors leave jewellery, watches and silver icons in the hope that St George will grant their wishes. You find yourself wondering what prayers were offered by the owner of the pearl necklace, the Camel Trophy watch or the Eiffel Tower pendant. It’s a particularly poignant question because the icon of Hagios, Georgios Koudonas, is famous for exorcising those ‘driven by evil spirits’. One chapel wall is still fitted with the iron rings that were once used to shackle particularly unwilling inmates.

Despite being so close to the incomparable grandness of Istanbul’s great sights – or perhaps because of it – this little monastery has a power all of its own. It is gaudy, glittery and kitsch, but after the overwhelming scale of the Aya Sofia or the Blue Mosque it is wonderfully unassuming. With its powder-blue dome, shimmering chandeliers and diminutive size, it feels a bit like walking into a Fabergé egg.

The Istanbul of today is still one of the most exciting, fast-paced cities in the world, but when the mind is overwhelmed by the scale of its great sights and the thrill of city life, there is a definite attraction in the dream of becoming one of Büyükada’s next exiles.

As I wandered back down the hill to the spot where Dimitri waited, I didn’t have to think long about what to wish for.”