Later, Peter Ustinov travelled to Istanbul with the vampish Melina Mercouri to win his second Oscar in the exotic - but unusually bad - heist movie, Topkapi. Bond also travelled to Istanbul to spy on the Soviet embassy from the city's underground cisterns in From Russia With Love, and to catch a cat-fight between two gypsy women, rivals in love.
But this fashion for seeking out oriental exotica in old "Stamboul" has its routes in the 19th century, when the diminutive French author, Julien Viaud, published Aziyadé , his risqué memoir of an erotic affair that would have been unacceptable in the West. Viaud, who wrote under the pen name Pierre Loti, later published another kiss-and-tell memoir, this time set in Nagasaki, which became the basis of Puccini's opera Madame Butterfly. Both books exploited the West's guilty pleasure in seducing alien beauty and nosing out the heady whiff of danger down darkened alleyways. Pierre Loti lit a lantern in Istanbul and lovers of loucheness have been drawn to that beacon ever since.
Today, even with Turkey poised to join the EU, Istanbul is the most Other of European cities. From the Pierre Loti Café, where Viaud used to wait for his mistress (though many now think Aziyadé a boy), the view down to the Golden Horn shows a skyline punctuated by minarets in a most elegant - but decidedly non-European - way. Take a cab into the city centre and you'll find a street layout very similar to that inherited by Mehmet the Conqueror when he seized Constantinople for Allah in 1453 and changed its name to Stamboul.
Dominating Istanbul is Sultanahmet, an architecturally stunning, if scruffy, promontory that in style and extravagance far outclasses St Mark's in Venice, the Palio in Siena or Les Invalides in Paris. There is Aigha Sofia, one of the world's oldest religious buildings, seemingly always on the point of collapse. Its red walls leached of colour, it rises like a jumble of child's building blocks. Mehmet added minarets when he rededicated the Byzantine basilica in 1453 and his successors added buttress after buttress to prop it up. But the ad hoc exterior is just a backdrop to the stunning display within, a vast golden vault pierced by shafts of light, Byzantine mosaics and shields covered in Islamic caligraphy.
All Sultanahamet's mosques, palaces, fountains and columns are grouped around a long, looping street known as Atmeydani Sok. What is not immediately apparent is that the Atmeydani was originally a hippodrome built for chariot races in the 3rd century -later enlarged by Emperor Constantine. Glimpses of this lost European culture, underlying the Islamic metropolis, are visible all over this city.
Literally underlying the Aigha Sofia is the Basilica Cistern, one of three vast man-made caverns constructed by the Byzantines to guarantee a water supply.Its intricate roof of herringboned bricks was supported originally by 336 26ft columns. "Lost" for centuries after the Turks took over the city, two-thirds of the cistern has been reopened as a tourist attraction. Music plays as fish swim in and out of the flooded columns, two of which are propped on huge carved Medusa heads, stolen from other Roman cities. In the words of St Jerome: "Constantinople was always clothed in the nudity of other cities."
The Blue Mosque and Topkapi Palace complete the major attractions of Sultanahmet. The coolly restrained mosque, one of the most famous in the world, was built over the old royal palace of Byzantine Constantinople and caused a scandal when it was completed in the 17th century because it sported as many minarets as al-Haram, Mecca's Great Mosque. Sultan Ahmet I protested that it was not his fault. He had told the imperial architect that he wanted a mosque built with gold minarets. But the Turkish words for "gold" and "six" sounded similar, and the architect, Mehmet Aga, was notoriously hard of hearing. Whether or not anyone believed this bluster, the Ottoman Empire made amends by paying for a seventh minaret to be added to Mecca.
Topkapi itself is one of the most unusual palaces you'll find in Europe. It is low, and arranged in pavilions around a series of courtyards. The story goes that when Mehmet the Conqueror built it he was having difficulty, having campaigned all his life, in coming to terms with the idea that he had achieved his goal. The Ottoman Turks no longer had to pitch tents in front of whatever city they were besieging. Nevertheless, Mehmet arranged the palace like a series of marble tents set in the open air.
Topkapi's kitchens, completed in 1465, are topped with 20 gigantic chimneys and resemble a vast Victorian factory. When Mehmet gave a party there could be up to 10,000 guests - and this at a time when England was pulling itself apart in the Wars of the Roses.
The heyday of Istanbul coincided with the Ottoman hegemony which stretched round the Mediterranean and into Egypt, Mesopotamia, the Crimea, the Balkans and to the gates of Vienna. Topkapi's Baghdad Pavilion was built in 1639 to celebrate the capture of that city, and the Pavilion of the Holy Mantle contains clothing, swords and hairs plucked from the beard of the Prophet, brought from Mecca.
But it was during its 18th and 19th-century decline that Istanbul became such a source of fascination to the rest of Europe. As the industrial revolution brought progress and prosperity to the West, Istanbul lived, literally, on capital. When it sought to catch up, late in the 19th century, it did so in grandiose gestures such as the Dombache and Ciragan Palaces that the royal family built on the shore of the Bosphorus, or in hotels such as the Pera Palas, built in 1892 to cater for tourists arriving on the Orient Express.
Frayed around the edges but monumentally grand, the Pera Palas still operates one of the world's first hand-cranked hotel lifts. The décor is superior railway hotel cum oriental palace, and the Grand Orient bar, lit by 19th-century chandeliers, is dark enough to hide its cracked cornices. Anywhere else in Europe this building would have been gutted and modernised, but then Istanbul is most unlike anywhere else in Europe.