When Indians dream of a golden city where their lives will be transformed, they dream of Bombay. When they hop freight trains away from the mud and the cows and the restrictions of caste and family, they head for Bombay. It is the gateway to all possibilities. Delhi may be the political fulcrum, Calcutta may enjoy greater cultural gravitas, Bangalore may be the new IT capital, but Bombay is indisputably India’s first city. Not only is it the nation’s economic powerhouse – accounting for almost 40% of the country’s tax revenue – it is the home of Bollywood, whose glamour dazzles every stratum of Indian society.

But Bombay is not only a great Indian city. It is one of the world’s great cities, magnificent in the manner of London and New York. It is contradictory, febrile, difficult, diverse and epic. It is sophisticated and venal, cosmopolitan and crass. It is endlessly energetic and fatally charming. Every week, there are hundreds of new arrivals. At 17m, the population of the city of Bombay is almost as big as that of Australia. In 15 years’ time, they say, it will be the largest city in the world.

Like all great cities, it has its problems. Faced with housing shortages, mounting debt and a transport crisis, the city fathers came up with a political masterstroke – they changed its name. Previously, it had been called Bombay; now, they said, it would be Mumbai. The name is derived from the name of the Hindu goddess Mumbadevi, and was offered to an increasingly chauvinist Maharashtrian community by a right-wing Hindu fundamentalist city government. But, like most political impulses in India, it has changed nothing. The irony is that only foreigners have taken up the new name with any enthusiasm, believing they are catering to Indian sensibilities. Yet most Indians, even most Maharashtrians, continue to call the city Bombay.

Adherence to the old name has done nothing to dull the appetite for such initiatives. The road committee, faced with deteriorating roads, is reported to spend 90% of its time on name changes. Nobody uses these names, either, but their selection is a useful diversion from tough political choices. The truth is, however, that Mumbai, as an entity distinct from Bombay, exists. To the writer Suketu Mehta, who grew up in the city, “Mumbai meant the people who came to wash the clothes or check the electricity meters. They were the ghatis – people from the ghats, coarse and poor . . . There were whole worlds in the city that were as foreign to me as the ice-fields of the Arctic or the deserts of Arabia”.

I set off to explore, heading north to the newest world, to the wealthy suburbs of Bandra and Juhu, home to some of India’s 300m-strong middle class. This is where mall culture has come to India, where air-conditioned families arrive in SUVs to prowl the international shops, the nondescript restaurants and the multiplex cinemas. But there is another world even here, a more glamorous world than that of bourgeois suburbia. This is where Bollywood and India’s new billionaire entrepreneurs come back to earth. This is where the icons who inspire the daydreams of millions live, shop and walk their dogs. Or, at least, have their servants do it for them.

At Olive Bar & Kitchen, the rubbernecking was so intense that people were in danger of choking on their bruschettas. Was that Malaika Arora Khan, the model and actress? Was she talking to Kamal Sidhu, the television personality? But for the Indian spin on the designer fashions, we might have been in Los Angeles or Cannes. The menu was Mediterranean, the prices were intimidating, and the highlight of everyone’s evening was celebrity-spotting. It wasn’t easy. Everyone here looked like they were someone.

Bombay’s nightlife, in yet another world, is now such an integral part of the city that it can come as a surprise to realise that it is a relatively recent phenomenon, having taken off in the early 1990s. The city is heaving with elegant new restaurants, trendy bars and serious clubs. Not long ago, Time Out began publishing a local edition, in the hope of chronicling this world. “In our first six months,” says its editor, Naresh Fernandes, “a new club seemed to open every week. In Bombay, every night is party night.” By one o’clock in the morning, the dancefloor at the Red Light is awash with revellers, arms aloft, swaying to techno. Many will still be here at five.

“People work hard in Bombay,” shouted Leena, a beautiful young thing who was something in marketing. “It is part of the ethos of the city. And now they are learning to play hard as well. We love to chill out.” Chilling out, she danced away in a flurry of energy with two boys in trainers and hoodies. I didn’t make it to 5am. A taxi took me home through the old streets in the south of the city. It was a revelation to see it virtually empty. Without the usual crowds surging along the pavements, or the torrents of traffic honking and jostling through the intersections, the magnificent Raj buildings, which are the backdrop of south Bombay, seemed to step into the foreground. If Bombay is tuned to novelty and change, it may be because it is so young. It was built in the 19th century to be the great port city of the Raj. But it was only at the turn of the century that it began to think of itself as an Indian Juhu Bandra city at all. Its architecture is usually described as Indo-Saracenic, though the journalist James Cameron may have been closer to theKalbadevi mark in describing it as “Victorian-Gothic-Saracenic-Italianate-Oriental-St Pancras-Gateway Baroque”. Over the years, ofIndia purists have condemned it, but time has a way of making any architectural style endearing. I love its extravagance and its confidence.

Indeed, Bombay is easily the most bombastic and engaging Victorian city of the British empire. Victoria Terminus is the most exuberant of its many monuments. Described by Jan Morris as “the central building of the entire British empire”, it is blessed with materials and decoration that would do justice to a cathedral, including Italian marble, polished Indian blue stone, elaborate stone arches and a riot of ornamentation along a facade more than a quarter of a mile in length. Gargoyles, peacocks, monkeys, and mongooses, busts of company directors, serpents, floral friezes, lions and tigers all soar upward in a frenzy of stonework to the dome surmounted by the colossal figure of Progress.

The city is crammed with such grandiose buildings. At Kala Ghoda, across the street from Red Light, is the grand facade of Elphinstone College, recently cleaned with startling effect. Next to it is the David Sassoon Library, whose street-level Italianate arches shelter pavement bookstalls where you can find both The History of the State Bank of Pakistan 1977 to 1988 and How to Make Love to Your Wife. Across the road is the grand Bombay Museum, formerly the Prince of Wales Museum, with its unrivalled collections of Indian statuary and painting.

Around the corner, along the eastern flanks of the splendid Maiden cricket ground, is yet another collection of imperial fantasies. They include the High Court, designed by Colonel JA Fuller of the Royal Engineers after a sketch he made of a castle on the Rhine, and the University of Mumbai, designed by the inimitable George Gilbert Scott, architect of St Pancras and the Albert Memorial. Scott never set foot in India: he completed the commission by post. His Rajabai Tower, modelled on Giotto’s campanile in Florence and decorated with figures representing India’s communities and castes, used to play God Save the King on the hour. Of such bizarre conjunctions are great cities made.

But all these – the swaggering colonial monuments, the museums and the art galleries, the smart suburbs of Bandra, the glamorous nightlife – all are irredeemably Bombay. Mumbai itself lies elsewhere, in the neighbourhoods that extend to the north, the neighbourhoods of the taxi-drivers and the washermen and the door porters and the kiosk traders. Its identifying features are not grand buildings, but people, the relentless tide of people who have migrated to this city over the past 150 years with their heads full of dreams.

You can find them in the great sprawling bazaar districts of Kalbadevi and Bhuleshwar, a river of people surging through narrow lanes of colour and aroma, of cows and handcarts. When you step into this river, you seem to lose your identity. You are carried along by its currents, buffeted by its banks. The river is never still. It is fluid, mutable, constant and unstoppable. The river is the lifeblood of this city, whatever they want to call it. The river takes you through bed linens and “shirtings”, where merchants recline on cushions, managing to eat, take phone calls, entertain their customers with tea and snooze – all at the same time. It takes you onwards into the alleys of silks and saris, where the air seems to vibrate with colour. A porter pushes a long cart loaded with obscure cotton sacks down an alley and the river parts momentarily, eddying round him, before closing again in his wake. You are swept forward through lanes of bangles and gold bracelets, past stalls of jasmine flowers and rose petals, along alleys of sandalwood and seashells, through markets of old gramophones and car parts.

When it finally disgorges you, on Grant Road or outside the Crawford Market, you feel you have been to another world, the world of Mumbai.

To recuperate, I retired to the Royal Bombay Yacht Club, where white-jacketed waiters attended with lime sodas. From the lounge, I could see the Gateway of India, opened in 1924, and used most tellingly for the departure of the last British troops 23 years later. The room is hushed and cool beneath big-bladed fans. Maritime prints adorn the walls, rattan chairs await sahibs and the library shelves are full of second-rate Edwardian writers. The clamour of Mumbai, filtered through the dusty leaves of mango trees, wafting through the open windows, is reduced here to a charming background hum. Only the slight whiff of the lavatory disturbs an otherwise ideal spot for a postimperial afternoon nap. The familiar stench of sewage, when the wind is in the wrong direction, is one of the ways that the different worlds of the city intersect. It is a pungent reminder to the members of the Royal Bombay Yacht Club, to inhabitants of the smart flats on Malabar hill, to the glamorous inhabitants of Bandra, that Mumbai exists. And that, in Mumbai – as opposed to Bombay – shit happens.

— Stanley Stewart was a guest of Greaves Travel

Travel brief

Getting there: fly to Mumbai nonstop from Heathrow with British Airways (0870 850 9850, www.ba.com), Jet Airways (0808 101 1199, www.jetairways.com), Virgin Atlantic (0870 380 2007, www.virgin-atlantic.com) or Air India (020 8560 9996, www.airindia.com), which also flies from Birmingham. Fares start at about £400. Where to stay: the luxurious and stately Taj Mahal Palace (00 800 4 588 1825, www.tajhotels.com) has doubles from £164. Or try the colourful, boutique-style Gordon House Hotel (00 91 22 2287 1122,www.ghhotel.com), which has doubles from £115. Packages: Greaves Travel (020 7487 9111; www.greavesindia.com) can tailor-make itineraries throughout India. Five nights in Mumbai start at £1,159pp, including flights, a city tour and an excursion to Elephanta Island. Other operators include Pettitts (01892 515966, www.pettitts.co.uk) and Cox & Kings (020 7873 5000, www.coxandkings.co.uk).

Where to eat, drink and dance: try the hypertrendy Olive Bar & Restaurant (00 91 22 2605 8228; dinner from £15), in Bandra; or, near the Gateway to India, Indigo (22 2218 2829; dinner from £15). The sophisticated, contemporary Masala Craft (22 6665 3366; dinner from £15), in the Taj Mahal Palace, serves the best Indian food you will ever eat. Dance the night away at Red Light (22 5634 6249).

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