Will Boris's airport sink or swim?

To some it is the perfect antidote to the frustration experienced by millions of Heathrow passengers each year and the misery of those who endure the drone of jet engines passing over their homes. A new airport built at sea that is easy to reach, passenger-friendly and doesn't keep anyone awake at night.

For others, it is an idea so far-fetched and outdated that it should be laughed out of court.

Boris Johnson, the London Mayor, who has described Heathrow as "a planning error of the Sixties", is reviving a radical idea: phasing out Heathrow and replacing it with a new airport on an artificial island in the Thames estuary. He has given a team at City Hall and a group of engineering consultants the task of re-examining the concept. "This study will look at the whole feasibility of an estuary airport," said a City Hall insider. "The Mayor wants to rule it in or out once and for all."

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The new airport has already been given a variety of labels – "Boris Island", "Heathrow-on-Sea", and the favourite tag of former transport secretary Ruth Kelly – "Fantasy Island". But though the idea of replacing one of the world's busiest airports may seem fantastic, plans for building a new hub in the estuary have existed for 40 years.

The Mayor envisages building the airport on reclaimed sand banks two miles off Sheerness, Kent, in waters 10 to 13ft deep. It would have four runways and could be expanded to six, dwarfing the capacity of Heathrow's two fully operational runways. Planes would take off and land over the sea, solving the blight of noisy engines at Heathrow and allowing the airport to operate around the clock.

Connecting the island to London and the continent with high-speed rail links would allow passengers to reach the capital in just over half an hour, about the same as it takes to get to Heathrow. Ferry links are also part of the mayor's plan. A similar scheme drawn up in 2003 envisaged tunnels linking the airport to the M2.

It may seem a mighty engineering feat, but know-how is not a problem – similar projects have been completed in Osaka and Hong Kong. The Mayor's plans are loosely based on the latter, a HK$20bn (£1.6bn) project on an artificial island that took six years to complete. Its biggest obstacle, unsurprisingly, is finding the money. Land reclamation and investment in roads and railways add billions to the bill. The plan produced five years ago predicted a cost of £31bn. Boris Island could need as much as £40bn.

The sheer expense would have seen it kicked into the long grass long ago, were it not for one thing – Heathrow. Throughout its 62-year life, London's main airport has been derided as a monument to Britain's make-do-and-mend approach to planning. Its origin was inauspicious – it opened in 1946 from an army surplus tent and had to wait until 1955 for its first permanent building.

The site was only chosen as an airfield in 1943 because it was a good spot from which to scramble fighter planes to protect the capital during the war. Since then, it has grown piecemeal while the capital has sprawled around it. The east-west runways ensure that the largest built-up area possible is affected by noise pollution.

"Heathrow has been a disaster in terms of planning and simply expanding it further would be typical of the way governments have tried to solve our aviation problems," said Sir Peter Hall, president of the Town and Country Planning Association and author of an influential 2006 pamphlet calling for the airport to be retired.

Critics of the estuary airport plan point out that we have been here before. While Mr Johnson is plumping for a spot off the Isle of Sheppey, another blond Tory, former prime minister Sir Ted Heath, preferred Maplin Sands off Foulness island. But Heath's plan, conceived in the 1960s, was abandoned because no one could be found to stump up the money.

The last time the Government took a look at the idea was in 2003. After examination, several proposals were dismissed as too expensive and ecologically damaging. Ministers also said that birdstrikes posed too great a risk to planes. In its place, they supported the expansion of Stansted and Heathrow.

Those involved in the proposals believe the Government was too quick to dismiss them. "It is not pie in the sky," said Mark Willingale, who led Thames Reach, one of the schemes considered. "The Mayor is right to start this debate again. The issue should turn to picking the right location. The estuary could potentially be the perfect site for an airport as infrastructure and housing are already there."

But the Government's determination to push ahead with a third runway is one of the worst-kept secrets in Westminster. Ruth Kelly used her final speech as transport secretary to rubbish the Mayor's big idea. "Boris may find his Fantasy Island airport a useful device to distract from the Tories' divisions on Heathrow," she said last month. "I call it politically opportunistic, economically irresponsible and environmentally disastrous."

Not all in her party agree. Labour MP Nick Raynsford remembers Heath's plan in the 1970s. "It was a mistake to abandon the project, though Heath may have selected the wrong site," he said. "Creating the new airport would be a 20- to 30-year project, so the Government has put it in the "too difficult" category. It is under pressure for a quick solution."

The support of business lies squarely with expanding Heathrow. Its leading cheerleader is British Airways, which has a stranglehold over existing take-off slots. For the airlines, expanding Heathrow is the cheapest option.

But an estuary airport might attract money from foreigners. Possible backing is already being sought from China. Behind the scenes, some airlines have shown interest in an estuary airport. The Virgin Atlantic boss Sir Richard Branson was said to be impressed by the Mayor's ambitious plans, though the company denies that it has promised any financing towards the project.

Expanding Heathrow will not be a cheap option, either – it is expected to cost around £13bn and would raise the number of annual flights from 477,000 to over 700,000, bringing noise, congestion and risk of an accident.

Moving London's main airport would have the added advantage of freeing prime real estate in west London, which would help with the South-east's housing shortage. Town planners predict 30,000 homes could be built on Heathrow's land.

A powerful regeneration argument has also developed. An estuary airport could create as many as 200,000 jobs in London's impoverished east.

Apart from the cost, though, there are practical problems too. The proposed location is perilously close to the wreck of the SS Richard Montgomery, which sank in 1944 while packed with 1,500 tons of explosives. But those concerns won't stop the army of Heathrow passengers trekking to their plane or residents plagued by noise from hoping Mr Johnson's Fantasy Island will one day become real.

Will Boris Johnson's Airport-at-Sea be declared feasible?