Liner notes: All at sea with John Walsh

It was probably pure coincidence that Céline Dion's "My Heart Will Go On" was playing on the PA system as our coach pulled up in Fort Lauderdale harbour and we first laid eyes on the Celebrity Solstice where she lay at anchor like a fat skyscraper. Beside it, the Titanic suddenly seemed pretty small fry. Nobody could look at this massive, towering, sleekly bulky ziggurat of maritime elegance, reflecting the hot Miami sunlight from 700 starboard windows, and imagine her coming to any harm. She seemed the match of any earthly manifestation of weather, wind or icy flotsam. (Not, of course, that you find many icebergs in the Caribbean Sea...)

The Solstice is the newest floating palace in the Celebrity Cruises kingdom, its 1,033ft-long, graceful white base piled topplingly high with 15 decks, 13 of which will house 1,426 guest cabins. With over a thousand crew members, the Solstice will cruise the world's oceans and seas, from Puerto Rico to Turkey, starting next month, with 2,850 paying customers on board. At 122,000 tonnes, it's the biggest ship ever to emerge from the Meyer Werft shipyard in Papenberg, Germany. And it will join a seemingly ever-growing industry of luxury ships – increasingly huge, surreally upholstered, ruinously expensive – that has become a phenomenon of modern UK travel.

Lots of people disparage cruises, for reasons of snobbery or ageism. Middle-class British travellers complain that cruises are full of the elderly, the moribund, the halitotic and the unsocialised, of retired publicans and bookies and their pampered memsahibs, enjoying a week of all-inclusive eating and drinking and culture-free drifting on badly decorated rust-buckets, punctuated by musical performances by the kind of entertainers who wouldn't get past the early auditions of The X Factor. It's an unfortunate image, as out of date as those idylls of shipboard romance in which blazered chaps from a Noël Coward drama pitch woo at marcelled virgins in tube frocks under the cruel moonlight. The cruise holiday has come of age.

A century ago, cruise ships were in their infancy. They grew out of ocean-going liners which, as the name implies, sailed on a single "line" between one port and one destination – such as the four-day crossing from London to New York. In the 1890s, Albert Ballin, owner of Hamburg-America, took the bold step of sending his transatlantic liners further south in the winter season, when the weather was bad. In 1900, he custom-built the first holiday cruise ship – the Prinzessin Viktoria Luise – so that the ship itself was the point of the holiday, not merely the means of reaching your destination. Other companies joined in, constructing special hull-strengthened ships and adapting them for winter and summer weather. Most notable was Cunard, which had run steam ships across the Atlantic since 1840; they came up with the slogan for cruise ships everywhere: "Getting there is half the fun."

The Titanic disaster, unsurprisingly, brought the cruise ship market to a screeching halt: for two decades, the only big liner-ships built were German. Cruise fans had to wait 23 years until the launch of the great French liner Normandie in 1935. Competitive shipbuilding broke out in the UK. The Queen Mary (at 81,000 tons, twice the size of the Titanic) had its luxurious maiden voyage in 1936, followed by the Queen Elizabeth a year later. But the market declined after the mid-1950s, when "Getting there is half the fun" no longer made sense in a world of fast airplanes. When Cunard launched the Queen Elizabeth II in 1969, the posh sea voyage had become as old-fashioned as the tumbril ride. The QE2 had a lot of style (but some disastrous swirly carpets and velour fabrics) and survived for 40 years as a kind of floating gin palace with penthouse cabins, butlers and sybaritic excess. Passengers routinely got through 73,000 bottles of champagne every year, and two and a half tonnes of black caviar – a third of the world's total consumption.

It's more than a decade since the Titanic movie was launched in 1997, bringing to gawping viewers the high style of 1912 liner design, Art Deco lounges and mahogany companionways. Viewers lapped it up, and craved to experience it for themselves, and a new cruise boom began. According to the Passenger Shipping Association, no fewer than 630,000 UK holidaymakers took either a river or ocean cruise in 1998. That's an increase of 22 per cent on the previous year.

Did none of them notice the film's denouement, when the ship disappeared under the Atlantic's waves, and 1,500 people drowned or froze to death? Perhaps the audience were too taken with the fixtures and fittings to care. But the cruise-ship boom of that year has gone on booming. Things speeded up after 2001: on average, nine or more new ships servicing US passengers have been built every year since then, to keep pace with demand.

Cruising has become crazily popular. In the last decade, the number of Britons cruising has doubled. The number of specialist travel agents dealing in cruises has increased exponentially. And the annual hike in cruise prices has fallen behind inflation. According to industry sources, 1.55 million Britons chose to holiday on the ocean wave this year, choosing from 50 cruise companies selling trips to 250 ports and harbours. The cruise market has become a major success story.

The market is dominated by three giant operators: top is Carnival Corporation, which owns 89 ships (most notably the Princess, Holland America and Costa lines) and have another 17 scheduled for delivery by 2012. Next comes Royal Caribbean Cruises Ltd, which deploys 38 ships under the Royal Caribbean, Celebrity, Azamara and Pullmantur brands. Third is Star Cruises, with 20 ships, including 12 under the flag of the Norwegian Cruise Line.

Down-river, so to speak, from these monsters are smaller operations – from Crystal Cruises, owned by the Tokyo-based Nippon Yusen Kaisha company, to Saga's Rose, Ruby and Pearl ships, owned by the Acromas group and aimed at over-50s (it helps that their ships u oall appear to be named after Edwardian barmaids) and the small easyCruise.com, owned by easyGroup, which offers rock-bottom prices, such as a seven-day cultural tour of Greece from £176.

As well as owning the Solstice and the rest of the Celebrity fleet, Royal Caribbean is responsible for the Freedom of the Seas fleet. Their flagship, Independence of the Seas, weighing in at 160,000 tonnes and with room to take 4,375 guests, is the largest cruise ship ever to operate from the UK – but its pre-eminence will soon be challenged by the massive Oasis of the Seas, to be launched next year. It will weigh an astounding 222,900 tonnes, and carry up to 5,400 passengers at full stretch. And if you quibble about the ship's name, on the grounds that oases are generally located in the middle of deserts, someone will briskly inform you that these names are arrived at democratically, after consultation with putative customers, so there.

What do you find when you go aboard one of these monsters? I arrived in Fort Lauderdale two days before the Solstice's official launch – the champagne bottle to be smashed by Professor Sharon Smith, a biological oceanographer and the dean of marine science at Miami University – and was given a privileged glimpse of its workings, along with an entourage of travel agents. Connoisseurs of cruise ships know the childish excitement you feel at marching up the gangplank, peering inside and catching your first glimpse of the opulence that will become overpoweringly familiar as the ship's secrets are unfolded. It's excessive to call cruise ships "floating cities" – they're more like floating villages where you greet the same faces day after day, explore little nooks and crannies from bow to poop, and stroll endlessly around the same village square.

Or, in this case, village green. Every ocean-going cruise ship has its own unique selling points, its slightly whimsical special features. One of the Solstice's features is the Lawn Club – half an acre of actual real-life grass, grown not from soil but from an "engineered porous lightweight growing media" that's apparently just as good. Cruisers can wiggle their toes on the grass as if they were standing in a Kent meadow rather than floating on several thousand fathoms of ocean. They can play golf or even (should John Prescott be on board) croquet.

At one corner of the lawn is the Hot Glass Show, another special feature to beguile that awkward half-hour between the 3.15pm swim and teatime. A quartet of expert glassblowers, from the Corning Museum of Glass in New York, demonstrate, with blowpipe and "gob" of molten glass, how their forebears fashioned rudimentary vases and decanters 2,000 years ago. OK, this may not strike you as the kind of entertainment you'd rush to see on the mainland, but when you're cruising, your conception of what's interesting or worth seeing changes drastically.

You could complain of feeling short-changed by the grass lawn and the glass blowing. I mean, on the P&O's Ventura ship, there's a training school in circus skills. On the Independence of the Seas, you'll find an ice-skating rink, a rock-climbing wall and a 40ft wave simulator, to help your attempts to surf. Oh, and a nine-hole miniature golf course. The massive new Oasis of the Seas will feature an outdoor amphitheatre, a park based on Central Park in Manhattan, two rock-climbing walls and – a little bathetically – a tattoo parlour. All passenger needs are catered for and anticipated. On the MS Deutschland, run by Peter Deilmann Cruises (specialists in "old world" glamour), the website assures potential passengers that "dialysis treatment is available on board". Who could ask for more?

Spend a day or two on the Celebrity Solstice, however, and it's hard to feel anything but wonder. On the outside it may resemble a horizontal tower block, but when you're on board, you soon succumb to its charms. Stand, for instance, on the main staircase around the sixth or seventh floor and look at the glass atrium that rises miles above you like the most glamorous hotel lobby. Look at the glass lifts gliding up and down, at the discreetly two-floor library with its clubland carpets and armchairs (and its books by Barack Obama and James Patterson). Look at the card-room, with its chessboards laid out for battle. Look at the jacaranda tree that has been casually suspended in the atrium to break up the sightlines (apparently it was a last-minute whim of the chairman's and cost a mere $500,000). Look at the restaurants, especially the Grand Epernay, a jaw-droppingly beautiful dining-room on two levels, coolly designed by Adam Tihany in grey and silver: chrome pillars, cream-grey chairs, striped grey cushions, huge glass-and-silver chandeliers. The total effect is of a shimmering, vestal purity, and impresses you as much over your peppered bison filet at dinner as it does during your banana pancakes and Belgian waffles next morning. There are nine other eateries to try, including one called Blu that serves "clean cuisine" (I assume they mean "unusually healthy", rather than "less dirty than the stuff in our other restaurants") to guests booked into the haut-ton AquaClass cabins.

The cabins, or "staterooms", are a far cry from the cramped little broom cupboards I remember from cruises when I was young. Each "stateroom" on the Solstice is large enough to contain a double bed, cupboard space, a wide sofa and desk. You can, to your surprise, do a lot of sprawling. The 32in Samsung television takes an Apple Mac Mini, so you can email your beloved from the Virgin Islands. The veranda is bounded on both sides by opaque glass screens that let through light but not prying eyes. The bathroom shower gives you room to move, and features a chrome "shaving ledge" for ladies to depilate their extremities in comfort.

A shaving ledge? Who came up with that little refinement? It seems the Celebrity group hired the services of five women advisers – a travel agent, a travel writer, a hotelier, a frequent cruiser and a first-timer – and asked what changes they'd like to make to the standard-size state room. They wanted (they said) everything larger, lighter, more spacious and more luxurious, from the mirrors to the bed linen, and the resulting design is hard to fault – though the fixed tap that lies immovably over the sink makes it impossible to perform manly feats of water-scooping and face-drenching; thanks, ladies.

It's the little things that count on holiday, isn't it? On a cruise, though, it's also the big things – like the Solstice Theatre, a stunning two-storey affair at the ship's prow. It gives the illusion of being the size of the Albert Hall, its sight lines are excellent, and the Cirque du Soleil-style shows it mounts are very professionally handled, if you're keen on that ribbony twirling-through-the-air schtick. Or like the main pool area, where the most sybaritic travellers hang out through the afternoon, dipping in and out of four pools, while fountains spurt up at random and a Cuban band plays "Jamaica Farewell" in an exquisite legato.

I could bang on about the high jinks in the Martini Bar (the lemon martinis are wonderful) and the elegance of the Cellar Masters wine-tasting room but you might think me a lush. I could bend your ear about the Galleria boutiques and the casino with its 200 machines and 20 gaming tables, but I found the former a posh version of Westfield and I cannot stand the tinny cheeping of Las Vegas-type casinos. I could mention the art gallery, the lovely Murano restaurant and the high-tech games in the X Club, the brilliant DIY pork stir-fry in the Oceanview Café and the Persian Garden steam-bath in the spa. But I think you get the picture. After half an hour I began to scrub off my prejudices against cruise ships, as though with an exfoliating glove. I began to see them as gorgeous floating hotels, stuffed like bran tubs with more treats and surprises, more sensory delights and sensuous experiences, than most holidays can offer -- and that's even before you've made landfall in St Kitts, or Haiti or the Azores.

A century after Alfred Ballin came up with the idea of the cruise, it's been expanded and refined to a gargantuan degree. And if we worry how much larger these ocean-going behemoths can possibly become, and how many crazed fun-seekers they can carry (5,000? 6,000? 10,000?) without risk of mass derangement, it's a concern that slightly ebbs away as you watch the sun dip into the scarlet horizon from the observation lounge, 16 decks above the unplumb'd, salt, estranging sea.

Getting there

The writer travelled on Celebrity Cruises' Celebrity Solstice (0845 456 0523; celebritycruises.co.uk). A nine-night Eastern Caribbean fly-cruise starts at £1,104 per person.

The price includes return flights from Heathrow to Fort Lauderdale, Florida; all transfers; one night's hotel accommodation; seven nights' accommodation onboard the ship in an Inside Stateroom; and meals and entertainment.

The cruise itinerary starts and ends at Fort Lauderdale and takes in San Juan (Puerto Rico), Basseterre (St Kitts) and Philipsburg (St Maarten). Prices in a Veranda Stateroom start at £1,256 per person. The Solstice's 11-night Eastern Mediterranean itinerary takes in Rome, Santorini, Mykonos, Istanbul, Ephesus, Athens and Naples/Capri, with departures from 4 May 2009 and prices starting at £1,765 per person.