It is a cold, autumnal wee hour of the morning in Istanbul and I am sipping a sweet, orchid-root-flavoured drink called sahlep and smoking a water pipe. I’m lurking outside a nargile (hookah pipe) joint on a small road called Ticarethane Sokak in what is known as the Old City or Historic Peninsula. This is where many of the city’s great monuments are, including the Hagia Sophia mosque, Topkapi Palace and the Hippodrome. This is also where Inspector Cetin Ikmen, the central character of my novels and subsequent BBC TV series The Turkish Detective lives. Like Ikmen, I enjoy wandering the city in the dark early hours of the morning. When only the hardiest, the mad, the bad and the protectors of the city roam the streets, so also do the phantoms appear.

In common with Ikmen, I disappear easily. I’m a woman of a certain age in a big coat and battered boots, and I walk like a man. I avoid eye contact. I’m here for the ghosts. Walking down Ticarethane Sokak, I join the main thoroughfare, Divan Yolu, and make my way past shuttered shops and silent coffee houses to the royal tombs on the corner of Bab-ı Ali Caddesi. This consists of a small cemetery for Ottoman princes and princesses, and a mausoleum that houses the remains of three 19th-century sultans – ranging in character from reformers to despots. Now they lie side by side in darkness, stared at by me through a metal grille. The ghost of Sultan Abdülaziz (1830-1876) – or maybe a white cat – briefly flits across my field of vision when I remember that he was found dead in mysterious circumstances.

Were this daytime, I’d probably carry on along Divan Yolu and head for the Kapalıçarşı (the Grand Bazaar) and attempt to locate the time portal that is said to exist at the centre of the great market, in the Iç Bedesten. But the bazaar closes at 7pm and so I can neither confirm nor deny the existence of that snippet of Istanbul esoterica at this time. At 3am, a quick pop back to Byzantium or forward to who-knows-what is denied to me. Instead, I head back the way I came and sit cross-legged on a bench beside the vast open space that was once the Hippodrome of Byzantium. This is approached via At Meydanı Caddesi, which is exactly opposite Ticarethane Sokak. Cetin Ikmen can see it from his apartment balcony but he, like me, prefers to go there.

Not even passing cops notice me as I let my imagination loose around the great Roman circus first constructed by the emperor Septimius Severus in AD203. Refashioned by the city’s first Christian emperor, Constantine the Great, in AD324, this was where the mighty Byzantine empire rewarded its citizens with bloody chariot races between political factions called the Greens and the Blues. Supported by opposing political parties, the rivalry between these teams was legendary, and in AD532 resulted in riots during which 30,000 people were killed.

I wish I could say that it’s rare to find someone who claims to have seen ghostly chariots racing round the Hippodrome at night, but I can’t because almost everyone except me has seen them. However, I’m not daunted and instead I close my eyes and listen. Faint at first, a hissing sound persists when I open my eyes again and I walk towards the Serpent Column. Set low in the ground in the middle of the Hippodrome, known as the spina, the column is now not much more than a short bronze candy-twist. But it wasn’t always like this. Created to commemorate the victory of the Greeks over the Persians in 479BC, it was once much taller and topped by three serpent heads bearing a solid gold bowl. Half-closing my eyes, I can see them writhe. As a friend to snakes, born under the sign of the Serpent Bearer, Ophiuchus, the disputed 13th sign of the zodiac, I am down with slithery ghosts.

Tendril by tendril, mist begins to roll across the city from the Bosphorus and the Sea of Marmara. Ships’ fog horns moan into the night like damned souls and I, together with a small tribe of local cats, head off towards the sacred precinct of Hagia Sophia. Now a mosque, until recently Hagia Sophia was a museum. Prior to that it was an Ottoman mosque, but it was built as a Byzantine Orthodox church in AD360. And though it has been rebuilt three times – the current structure dates from AD537 – a sacred building has stood on this site for almost 17 centuries.

My small cohort of the famous Istanbul cat population don’t give a damn about history and are only hanging around with me in case I magically produce some food. But I like their company, their soft yowls, their furry bodies winding themselves through my legs. Echoes of long-dead Byzantine emperors and empresses float by. This whole area was once the Great Palace of the Byzantines. Now deep underground, the Great Palace contained a room made entirely from red porphyry stone where every true member of the royal family was born. It’s where the expression “born to the purple” originates.

This is a place thick with legends. They include stories about tunnels connecting the great church to the royal box in the Hippodrome, about slighted empresses blinding unfaithful lovers, and the production of aphrodisiacs, magical spells and youth-restoring skin creams. However, my favourite myth is the one concerning what happened in Hagia Sophia on the night of 29 May 1453.

After a siege lasting 53 days, the Ottoman Turkish army under the command of the 21-year-old Sultan Mehmet II entered what was then called Constantinople and broke into the church. Hagia Sophia’s priests, who had been praying for deliverance from the Turks day and night for weeks, neither looked at the young sultan as he rode his white stallion up to the altar, nor did they cease their devotions.

It is said that, still praying, they turned away from Mehmet and disappeared into the walls of the building where they remain to this day, awaiting the return of their once mighty empire.

Amid the shifting outlines of the mist-robed building, you can almost believe it, and I wonder what, if they are still there, those priests have been doing all this time. I imagine them as etiolated, black-clad figures, their ancient eyes ever searching for a future that will never come. The cats, whose ancestors predate the clerics by some margin, may and probably do know, but another human has materialised and is feeding them, so my presence is now irrelevant.

I cross Divan Yolu and return to Ticarethane Sokak and the home of my hero, Cetin Ikmen. As I walk into the mouth of the small thoroughfare, the night closes round me and I disappear into the darkness.

Barbara Nadel’s latest Ikmen mystery, The Darkest Night, is published by Headline (£22). To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.