In the event that it is ever actually built, the Freedom Ship, "the world's first mobile, floating city", will have to be constructed at sea: there isn't a port on the planet that would be big enough to accommodate it. "Imagine a mile-long stretch of 25-storey buildings in New York City; now imagine that floating on the water," one reporter wrote, after detailed plans were released a few years ago. As it turned out, "imagine" proved a well-chosen verb. But there was no denying the breathtaking ambition of the Freedom Ship's designers: artists' impressions showed a gargantuan, flat-bottomed slab of glass and concrete, 340ft high, capable of housing 60,000 people and topped with several aeroplane runways. The QE2 was pictured alongside, for comparative purposes; it looked like some kind of tugboat.

On board the Freedom Ship would be schools, hospitals, banks, light manufacturing industries, shops, restaurants and 200 acres of open space, according to its chief engineer, a modern-day Noah from Florida called Norman Nixon. There would be no local taxes. "It will follow the sun - it will be better than a land-based city," the head of marketing told anyone who asked. By 2002, 3,000 families and businesses had reportedly signed up to live and work on it, although Nixon himself adopted a wry tone that seemed to acknowledge the absurd vastness of his plans. "As soon as I build this joker," he told Fox News, "I'm going to retire and live on it."

But some things are easier said than done, especially when it comes to building giant floating cities weighing 2.7m tonnes, and recently a downbeat statement signed by Nixon appeared on the Freedom Ship's website. It uses too many quotation marks, and devotes several lines to a bizarre attack on Wikipedia, but the gist is clear. "We were... contacted by a group of people who we thought in the beginning had a serious interest in the ship [but] wanted nothing more than to use us for a 'scam'," Nixon claims. There then follows a string of accusations and allegations of financial impropriety: "So, as you might guess, we have a major lawsuit against everyone involved." Things are at a standstill "while the lawyers get to work. We could get moving if we could find $150m, but as of now we don't have that kind of money." Nixon is currently busy running a long-shot campaign for the US presidency.

Perhaps you need to be an eccentric to dream on this kind of scale, and maybe it's inevitable that you'll attract scam artists along the way. Several times, in recent decades, different groups have proposed building floating cities at sea, but almost always their plans have collapsed amid acrimony, alleged criminality or lawsuits, along with a chronic lack of funds. Mostly, they have been Americans of a libertarian bent, intent on escaping the yoke of government, especially taxes, and embarking on a kind of endless retirement cruise. But last month the idea re-emerged in a different form: what if colonising the oceans were to become not just a libertarian escape fantasy, but an environmental necessity?

A young Belgian architect, Vincent Callebaut, unveiled Project Lilypad, a vision of a "floating ecopolis", shaped like a giant waterlily, that could house tens of thousands of people forced from their homes by rising sea levels. "It will be one of the major challenges of the 21st century to find ways to accommodate environmental migrants," he says. According to the UN's International Panel on Climate Change, sea levels will probably continue to rise for centuries even if greenhouse gas emissions are stabilised; they could rise by as much as 81cm this century, enough to devastate areas such as the islands of Kiribati and the Maldives, and parts of Bangladesh. The Netherlands is spending huge sums to reinforce its dykes, Callebaut notes, and the United Arab Emirates is building expensive new land, near sea level, in the Palm Jumeirah reclamation project. But both solutions can only ever be sticking-plasters. "The Lilypad," he says, "would be a long-term solution to the water rising."

The notion is ridiculous, of course: another chapter in the long history of urban futurology, according to which we were all supposed to be travelling in airborne bubble-cars by now. And yet there's something bewitching about Callebaut's designs. The Lilypad is calming even to look at; it feels like something that might have evolv ed naturally. The steel and glass that dominate the Freedom Ship are relegated to second place behind the flowing contours of three "mountain ridges", covered in vegetation and hollow within. Where the real-life lily is weighted and balanced by its central submerged stalk, the Lilypad has a glass-walled, underwater, bowl-shaped space that could be used for commercial and leisure facilities.

Technical details are notably lacking from Callebaut's vision - he doesn't even pretend to estimate how much it would cost to build - but the general idea is that it could be self-sustaining, using various forms of renewable energy and collecting and purifying rainwater in a central lake. Its titanium dioxide skin could absorb carbon dioxide from the atmosphere. "The whole city is covered by a stratum of suspended gardens," Callebaut says. "The goal is to create a harmonious coexistence between humans and nature." One of his images pictures Lilypad floating between the islands of the Maldives. It doesn't look like an emergency solution to a nightmarish crisis: it looks like a beautiful addition to the view.

But it didn't take long for the old problems of egos and allegations of underhand behaviour to assert themselves. The media excitement over the designs overlooked the striking similarity they bore to Mermaid, a project created by a Danish architect, Julien de Smedt. Mermaid was envisaged as something far more modest: a floating "wellness resort", with a water park at its centre. It was designed to accommodate far fewer people, but that wasn't enough to prevent De Smedt from growing angry at the attention Callebaut's images received. "We have been running a case on him," says De Smedt, whose firm has been investigating Callebaut's other work to look for instances of plagiarism. "He's a strange character. His project is on another scale, but it's the same: the shape, the three peaks, everything. In my view, it is totally driven by our work." (When I asked for his response to this allegation, Callebaut stopped communicating with me.)

The idea for the Mermaid, De Smedt says, came to him almost by chance: "Our client wanted this wellness resort, but he didn't feel it was suited to Denmark, so he started asking the question of whether we should think of another location. I suggested designing an island." A Middle Eastern investor is now interested, and engineering feasibility studies have been carried out, De Smedt says - all of which suggests another difference that may soon distinguish the Mermaid from the Lilypad, and from every other fantasy of a floating metropolis that anyone has ever entertained: it might really exist.

People have dreamed of colonising the oceans for decades, but they've generally glossed over the practical challenges. Their minds have been on higher things - specifically, creating new nations to which their founders could escape and live in peace, untroubled by the actions of governments, or by other people in general. Their projects have had names such as the Free State Project, Laissez-Faire City, Libertocracy and New Utopia. As is common in the world of libertarian politics, the language in which they speak of their plans tends to be tetchy and misanthropic, dripping with contempt for the ordinary herd. "Most people never leave 'home' - they grit their teeth and simply endure whatever their 'home' government throws at them, as if no possible alternative exists," writes Prince Lazarus Long, ruling monarch of the as-yet nonexistent principality of New Utopia, which he plans to build on concrete platforms perched on the Misteriosa Bank, a submerged atoll in the Caribbean. (Long was born Howard Turney; he changed his name to that of a character in a science fiction novel.) "A small - but growing - number of individuals... refuse to confine themselves to the advantages and drawbacks of just one country," he continues. Taxation will be illegal in New Utopia, and Long claims that more than 3,200 people have paid a fee to register as the first citizens. Unfortunately, there will first be some hurdles to overcome: in 2000, the US Securities and Exchange Commission declared New Utopia to be a "fraudulent nationwide internet scheme", accusing Long of making tens of thousands of dollars from the sale of bogus securities. He insists it is legitimate, and is ploughing ahead.

On a handful of occasions, such schemes have become reality - perhaps most famously in the case of Sealand, the unofficial "micronation" on a structure off the Suffolk coast that was used as a second world war fort. Sealand's ruler is Prince Roy, aka Paddy Roy Bates, who now lives in retirement in Spain; in 2006, a fire caused extensive damage, and plans are reportedly underway to sell the platform and open an internet casino there.

Yet the dream of creating a thriving new nation on the sea refuses to die. Earlier this year, Peter Thiel, the entrepreneur behind the web-based payments system PayPal, donated $500,000 to inaugurate the Seasteading Institute, which aims "to establish permanent, autonomous ocean communities to enable experimentation and innovation with diverse social, political, and legal systems." Although motivated by similar libertarian impulses, the institute does seem, for once, to be giving extensive consideration to the engineering work such dreams would require. The strategy is to start small and scale up: from "PintStead", a tongue-in-cheek structure small enough to float in a beer glass, to the fish-tank-sized AquariumStead, to PoolStead, to CoastStead, "a floating home that can go anywhere", which they plan to build and exhibit off the US west coast, starting next year. (After that, they plan to explore larger combinations of multiple floating homes.) Meanwhile, at Seasteading.org, enthusiasts discuss a plethora of issues, from farming algae to produce fuel, to procuring surface-to-air missiles as a defence against attacks from established states.

It is ironic that the notion of the floating city should arise as a potential answer to the problems caused by global warming, since the libertarians responsible for the earlier ocean-colonising visions have tended to despise government-led initiatives, including those targeting climate change. But building floating homes is an idea with its own history, too, primarily in the Netherlands: near Maasbommel on the banks of the river Meuse stand almost 40 three-storey homes, tethered to the ground, designed to rise with the water whenever the river floods. (Responding to a problem by seeking to accommodate it, rather than eliminate it, is a characteristically Dutch approach: it is, of course, how the Netherlands deals with prostitution and drugs, too.)

Earlier this year, two architecture graduates at Harvard made a related - if rather more fantastical - proposal for post-Katrina New Orleans, envisaging homes that could float when required. "Rather than considering the river an unwanted guest, welcome it in," they suggested. "Allow the city to wander through the river... Individual dwellings bob, tethered [by] umbilical cords through which potable water, electricity, sewage and telephone connections continue uninterrupted. When the water subsides, depositing the city in a new arrangement, a post-diluvian landscape emerges," they went on. "The city's historic economic stratification is blurred." One can envisage a few practical problems with a street layout that changes every time a city floods. But it's something to think about.

Environmental campaigners tend to be scornful of ideas such as Callebaut's Lilypad, which, they say, offer not solutions to the climate crisis but dreamy distractions that encourage us to think we might get away with not having to make drastic alterations to our lifestyles right away. "The idea that we can somehow take humanity, scoop it up and place it on an island that's self-sustaining, and therefore that we can continue to exist as we were - well, let's just say that it's deeply unrealistic," says Ben Stewart, a Greenpeace spokesman. "Perhaps it would be possible for a small, elite proportion of humanity. But what we should really be talking about is trying to protect a planet that is perfectly capable of sustaining us in perpetuity... The coming century isn't going to look like an HG Wells novel, where, if we lose the battle, we move to another planet or to the oceans. It's not going to look like that. It's going to be a large number of people dying."

Besides, it's hard to imagine that life on a Lilypad would really be such a paradise. Surely they'd soon become floating refugee camps, housing people the rest of the world would prefer to forget - prisons for an unrooted, essentially homeless underclass? Even as an elite getaway, it's not clear that a floating metropolis would be that much fun. Cruises, after all, are an acquired taste, and there's something unavoidably fake and claustrophobic about even the finest ships. On board QM2, for example, according to publicity material, "sybarites can enjoy the rejuvenating treatments of the world-renowned Canyon Ranch Spa Club... Or how about a visit to the planetarium? A wine-tasting seminar? Or a walk down history lane at the Maritime Quest exhibit? QM2 is a veritable City at Sea, with everything from virtual-reality golf [and] a basketball court to a bookshop." Now imagine living there all year round.