Travel: Where dreams of Byzantium come true: For more than 2,500 years, Istanbul has been Europe's gateway to the East; Angela Lambert waited only 35 years to visit it

There cannot be another city in the world with a more beautiful or more strategically important setting than Istanbul. On the one side Europe, on the other side Asia, and in between the wide flow of the Bosporus on which every kind of vessel, from mile-long oil tankers to brisk little ferries, plies its trade.

Formerly known as Constantinople and before that Byzantium, the city has straddled this vital shipping lane since the 7th century BC, controlling access from Russia and Asia into the Mediterranean and vice versa. For more than 2,500 years it has been the pivot for trade and culture between East and West, a city both Ottoman and classical, Oriental and Western, Arab and Christian, usually both at the same time. This melee of influences gives its buildings and people a quite exceptional richness and fascination.

Standing on the pavement as a shoal of yellow taxis, honking cars, battered old vans and suicidal jaywalking people pour past, you can look up to the domes and minarets of the Hagia Sophia mosque, piercing the deep blue sky as they have since the 4th century, and feel that you and they are at the still centre of the turning world.

Istanbul is like a cross between Bombay and Los Angeles: partly a Third World city and partly a modern trade centre. It is noisy, dusty and argumentative, with starving kittens mewing at your feet and shopkeepers calling their wares and beckoning urgently from every nook and cranny.

Traffic gridlocks on the main thoroughfares or moves with terrifying swerves and at breakneck speed along motorways and flyovers. 'I've never seen traffic like it anywhere,' I said to a Turkish friend. 'Do many people get killed?'

'Many,' he said laconically, overtaking a taxi while doing 60mph on the inside lane.

In 1946, after the Second World War, Istanbul's population was barely 1 million; today it is 7 million. The incomers are economic refugees from the Turkish countryside in search of work, money, food, shelter, for rural Turkey is still positively medieval. Istanbul has housed the newcomers better than might be expected. On the city's outskirts apartment blocks spring up, the lowest floors already occupied, washing flapping over the scaffolding, carpets draped across concrete balconies even while the upper floors are being built.

There are two things every traveller comes to see - three, if you include the legendary Grand Bazaar at the heart of the old city - and they can be seen in a long weekend. The first is the Topkapi museum; the second the mosque of Hagia Sophia.

The Topkapi Palace was built by Sultan Mehmet II (the Conqueror) after the fall of Constantinople in 1453, and added to by successive sultans. It stands on a low hill that protrudes into and dazzlingly overlooks the Bosporus. It was home to the Ottoman sultans, their families, attendants and harems, for the next four centuries. Like Moscow's Kremlin, it is itself a walled city: palace and stronghold for the sultans, showcase for their fabulous wealth, safe haven for their armour, secure setting for their private luxuries and atrocities.

The Topkapi is now a museum, open daily till 5pm (entrance costs 81,000 Turkish lire - less than pounds 2). You approach along a series of parks and shady walks, protected by rustling trees. Passing through its first solid iron gate, you enter a courtyard ringed by a series of low buildings. On the right are kept the Sultan's carriages, starting with latticed harem carriages from the 18th century, plump seats decorated with dark turquoise satin and heavily embroidered with gold. Another is armoured, lined with red satin and adorned with a border of crescent moons.

The Gate of Felicity, flanked by gorgeously tiled plaques in yellow, turquoise and stinging green, leads to the next courtyard where audiences were held, ambassadors received and administration carried out. Inside it is a vista of marble floor slabs and shady walks. The sultan's throne is a huge, magnificently canopied sofa without legs, covered with gold embroidery. Nearby a fountain splashes - to obscure, it was said, the cries of disappointed supplicants or those being flogged for their temerity.

Behind this lies the inner palace, where family servants lived and the sultan had his private quarters. The whole complex is roofed with a series of shallow domes covered with sheets of beaten lead. By now one is so accustomed to magnificence that it is almost a surprise to find they are not gold.

Next, on the right, is the imperial treasury. Wealth unimaginable, sapphires the size of fists, diamonds that reflect one's face, daggers encrusted with precious stones - the excess is staggering and quickly becomes meaningless.

This is wealth beyond vulgarity, beyond greed, beyond computing. A single pendant contains three emeralds worth pounds 1m each - just one ornament among hundreds. A large American woman in tight shorts walks up to each glittering showcase, fires a quick burst from her camcorder, and moves on without a second glance. A family of headscarved Turkish women watch her serenely, then turn aside to giggle.

Everything is encrusted with diamonds or pearls, made of jade or crystal, ebony or ivory or tortoiseshell, inlaid with gold. Everything is real, solid, priceless. A sultan's throne, 5ft high and nearly as wide, is made of pure gold. Quite soon one becomes sated and begins to pay attention to the crowd: noticing the affection of a young Turkish father for his baby. He sits in an alcove beaming at it, the baby beaming joyously back. A gold-plated cradle in the next room shows that the imperial babies started as they meant to go on.

Barbaric practices were carried out here. When the new sultan was chosen (with much influence exerted by the women and eunuchs, forever plotting and conspiring) he had all his rival brothers murdered. Absolute power brooks no opposition.

We make our way to the Konyali, the Topkapi's own excellent restaurant. On the opposite bank is Asia; behind us the sea of Marmara, while shipping going through the Bosporus eventually reaches the Black Sea. We order kebabs and rice at less than pounds 3 a head; refreshing apple tea and honeyed Turkish pastries cost pounds 1. Skinny tabby cats lurk under the tables. One gnaws at the remains of a leg of lamb, hardly able to believe its luck.

After lunch we stroll around the harem quarters, their latticed windows giving a tantalising glimpse of the world outside. The rooms are exquisitely tiled. Huge sprawling sofas convey an air of suffocating indolence. Nearby is the circumcision chamber, where the young princes were snipped in a most splendid setting. Finally, a roomful of relics of the prophet Mohamed . . .

a letter he wrote, a hair from his beard, the imprint of his foot (large, with deep toe-prints). I am surprised at the easy tolerance that lets me view them, bare-limbed and bare-headed, but the Turks are relaxed about their religion; fundamentalism has gained little foothold here as yet.

In the evening our Turkish friends take us for a drive along the Bosporus, past crumbling (and sometimes restored) 16th, 17th and 18th century 'country' villas, to a fish restaurant. We sit almost on the pavement; traffic thunders past; we have to shout to hear one another above the din.

Street vendors offer balloons, long-stemmed roses, funny hats; a little girl does an undulating dance. The meal consists of freshly-caught fish; prawns, octopus and a local delicacy called kalkan which, grilled, seems the most subtle and delicious fish I have ever tasted.

Next day we go to the Hagia Sophia, the vast domed mosque that that I have longed to visit ever since I read Pevsner's description. Its immense, soaring span must have been astonishing in the 4th century and is no less amazing now. The main dome, 56 metres from the floor, is supported by two half-domes at either side, themselves supported on pillars that - after 1,500 years - are leaning sideways under the strain.

At the far end of the mosque light pours brilliantly through abstract stained-glass windows. At the apex of this former church is a huge mosaic of the Virgin and Child. Other mosaics - Christ with John the Baptist, sorrowful and rugged - appear elsewhere. What happened to Islam's former tolerance, I wonder?

In a marble pillar close to the entrance is a hole that is perhaps 3in deep, gouged by the fingers of innumerable pilgrims who were told that those who touched it would have their prayers heard. I, too, push my finger in, billionth in an unseen procession of hope.

The centre of the vast space is lit by daylight, but several huge chandeliers hang low to illuminate it after dusk. Even so its upper reaches are dim and remote. Only by walking round are its marvels revealed: the slabs of marble laid like veneer against the walls; a steep ramp (not stairs) that winds up to the gallery, its stone slabs polished to an oily smoothness, from which one can look down upon the immensity of the great mosque and the busy hive of people milling below. The walls are elaborately painted and decorated with pattern upon pattern upon pattern, here and there a cross crudely incised into the stone by a pilgrim.

Istanbul crowds the imagination with teeming millennia of history. It is also a modern city of surging energy where one is constantly brought up short by the individual, the human and the unexpected.

It is quite something, to wait 35 years to visit a city and not be disappointed. I was not.

FACTFILE Getting there: The cheapest flight to Istanbul on Turkish Airways is pounds 210 return (booked a month in advance); departures are from Heathrow (071-499 4499) and Manchester (061 489 6123). British Airways has a special offer on flights to Istanbul: book before 2 November for a pounds 178 return ticket. Departures are from Heathrow (0345 222111).

Where to stay: Hotel Merit Antique is modernised and in the old city: double rooms with bath and breakfast are pounds 85 a night (010 90 212 513 93 00).

Further information: Most museums and mosques open 9.30am-5pm; bazaars 9am-9pm.

(Photographs omitted)