Imagine a giant room, with giant glass windows, filled with sculptures of such beauty that they are hailed as one of mankind's highest achievements. Imagine this capacious space facing one of the world's exquisite monuments of classical art. Now place it against an Attic sky, a sky so bright that it not only illuminates the monument's marble surfaces, but floods the room with natural light. You have just imagined the Parthenon Gallery of the New Acropolis Museum in Athens, at the foot of the masterpiece that epitomises the Periclean age.

After more than 30 years of preparation, procrastination and acrimonious debate, the building, which once seemed like a far-fetched dream, a last resort of the romantically inclined, is finally nearing completion. This month, labourers working under the watchful eye of the distinguished archaeologist Dimitrios Pandermalis began laying the £94m behemoth's marble floors. Soon the curtain-wall façade of the three-storey edifice will be up; in November, British metalworkers (led by a man who, like Lord Elgin, is a Scot but, I am assured, is no admirer of him or his depredations) will begin installing the museum's gargantuan glazed-panel roof.

By next summer, visitors will no longer have to view treasures in the cramped confines of the current museum, which was hastily erected on the Acropolis hill after the Second World War. The new building, designed to house all the Par thenon marbles - including the 88 plundered sculptures that, thanks to Thomas Bruce, the 7th Earl of Elgin, are now in the badly lit British Museum - will have opened its doors.

The possible reunification of the marbles makes even Professor Pandermalis, a man of infinite restraint, bubble with delight. "For the first time," he says, six years after he began overseeing the museum's construction, "we'll have a place appropriate for the sculptures of the Par thenon." Not only would Phidias's monumental procession frieze and other carvings be displayed within view of the iconic architecture they once decorated, but also - Pandermalis enthuses, as we walk through the museum building, up ramps that replicate the approach to the temples - they would be arranged as they originally appeared. Pointing to a series of apertures in the walls, he tells me how the temple's cella, or inner room, has been reproduced in the museum. "It exactly mirrors the building's dimensions and orientation down to the last millimetre."

But what if the British Museum won't collaborate? (It has so far shown no inclination even to discuss the issue, let alone change its mind.) Then, says Pandermalis, there will be big, empty spaces. "Maybe, in those places, we should just say, 'Go to London,'" he murmurs, before embarrassment prompts both of us to change the subject and emote over the stunning view of the Acropolis instead.

In the always bitter, often ugly, battle over the marbles, nothing has threatened to shift the debate as much as this. Each day, as the 14,000-square-metre building goes up, Athens is literally chipping away at the argument that the sculptures are better off in the sombre Duveen Gallery of the British Museum in London. The New Acropolis Museum, designed by the Swiss-American architect Bernard Tschumi and co-sponsored by the European Union, will finally put paid to the claim that modern Greece has nowhere decent enough to house the remains of its golden age. For the Greeks, it will be the ultimate propaganda tool, more eloquent than any number of complicated legal arguments.

"Soon we'll be able to accelerate efforts for the marbles' return, find a different approach, perhaps a friendlier one," pronounced the Greek culture minister, Georgios Voulgarakis, when he visited the site earlier this year. A consummate politician, Voulgarakis is not one to speak out of turn. In recent weeks, perhaps fearing the "evil eye", he has refused to comment on how Europe's longest-standing cultural row might be handled in the critical months ahead.

But then, in the arena of contested antiquities, events are in many ways moving faster than policies. In his relatively short time in the post, Voulgarakis has had more lucky breaks than any of his counterparts to date - breaks that may well have an impact on the fate of the Par thenon sculptures.

The first came with an unexpected offer to return a chunk of the decorative floral band that once adorned the Erechtheion to Greece. For decades it had been in the possession of Birgit Wiger-Angner, a Swedish woman who had inherited it from her father, who, in turn, had been given it by an uncle, a former naval officer who had acquired the relic on the streets of Athens in 1895. Handing the fragment over this year, Wiger-Angner said that she could not, in good conscience, keep "what rightly belonged to the Greek people".

In July, the world's richest art institution, the J Paul Getty Museum in Los Angeles, went further. In a ground-breaking move, it agreed to surrender two prized antiquities to Greece. For years Athens had tried, and failed, to reclaim the artefacts, an ornate 2,400-year-old tombstone and a votive relief dating from the 6th century BC, both removed by looters in the 20th century. But after three months of exhaustive negotiations - and with Greece promising a merry-go-round of other objets d'art on long-term loans - the Getty board announced that "it would be right" to yield the pieces.

This repatriation closely followed not only similar agreements with Italy, but an extra- ordinary decision in February by New York's Metropolitan Museum of Art to return a number of contested items to Rome. Not least of these was the Euphronios krater, its most prized ancient Greek vase, for which trustees paid a sensational $1m in 1972. Announcing the move, the director of the Met, Philippe de Montebello, said that although he remained against restitution, he knew that, in this case, the request for repatriation "was not going to go away".

Then, last month, it was the University of Heidelberg's turn. After years of being beseeched by Athens to hand over the marble fragment of a foot belonging to the Parthenon's northern frieze, the university conceded to the demand. At a ceremony to welcome back the sculpture, Voulgarakis could barely contain his excitement. "The Parthenon marbles have started to come home," he declared. "This is the first time that a request for their return has been accepted. The silent agreement among those in possession of them has been broken."

Culture in transition

There has undeniably been an important change in international cultural policies. Attitudes towards disputed items in museum collections have altered significantly, and dubious acquisitions policies are increasingly being questioned. As prosecutions have grown, restitution claims have flourished both in number and sophistication - testimony, say campaigners, to the growing power of cultural politics in the 21st century. All of which makes a nonsense of the argument that returning the Parthenon marbles would open the floodgates to other claims. The floodgates are opening anyway.

"We see the prevailing cultural environment as one of transition," says Christopher Price, deputy chairman of the British Committee for the Reunification of the Parthenon Marbles, "from one that emphasised ownership, retention and monetary value to a new era in which context and voluntary agreements to co-operate have become the engine of development."

In this spirit, the Greeks have "put aside" the issue of ownership and have proposed instead joint curatorship of the marbles through the establishment of a branch of the British Museum in Athens. And they are willing to be generous. In return, London can have its pick of countless treasures - the British trustees have already been promised any number of Minoan antiquities for a major exhibition in 2009.

"Greece has made it clear that it is seeking collaboration and cultural co-operation for any solution to the reunification of the Parthenon sculptures," says Eleni Cubitt, who has run the British Committee for the Reunification of the Parthenon Marbles from her north London home since 1983. "The director of the British Museum will realise that it will be to his own benefit to seek a solution." Already, she says, the cultural establishment has undergone a change of heart - imperceptible but growing - as the benefits of "collaboration" and "joint curatorship" become more apparent. All polls taken over the past decade have shown that a majority of the British public wants the marbles back in Greece. In a September 2002 MORI survey the number of Britons supporting the return of the sculptures exceeded the number who want them kept in London by eight to one.

Yet, despite this - not to mention the common sense of housing all the artefacts belonging to a single structure in one place - the idea of a progressive international cultural policy appears to have bypassed Tony Blair's government. New Labour has preferred to follow the lead of the British Museum and its civil-servant allies at the Department for Culture, Media and Sport. For its part, the museum sticks to its argument that the division of the surviving sculptures is of "maximum public benefit for the world at large". Its website claims that this "allows different complementary stories to be told about them, focusing respectively on their importance for Greece's national heritage and world cultural history".

Campaigners for the return of the marbles to Greece say it is dis ingenuous of the government to continue to take its cue from the British Museum when it knows the trustees are against even discussing the matter. "It is the British government and not the British Museum that is responsible for cultural policy," says David Hill, who presides over the International Association for the Reunification of the Parthenon Sculptures.

"The carvings were placed in the British Museum by the British government. The government appoints most of the trustees to the museum and is responsible for the legislation that dictates how the museum is run."

Mounting pressure

The political cowardice over the issue has been matched only by political hypocrisy. Time and again in the 1980s, when Labour MPs could afford to be honest, there was widespread support for the return of the sculptures, with both Neil Kinnock and Michael Foot promising, as opposition leaders, that they would go back.

In 2000, an Economist poll showed that 66 per cent of all MPs would vote for the sculptures to be returned to Athens. Of that figure, 84 per cent were Labour. In 2002, the then minister for health and current minister for culture, David Lammy, went further. In a letter to Professor Anthony Snodgrass, the historian who chairs the UK reunification committee, he wrote: "I would like to take this opportunity to express my support for you and the work of your organisation."

On 10 October, a Commons cultural select committee began taking evidence in an inquiry set up to assist the government on future legislation for museums and cultural property. Among the issues expected to be discussed are art looted during the Holocaust and restitution claims by "first peoples" - claims that have soared since the British Museum, at Blair's prompting, amended its rules to allow the return of indigenous human remains from its collections.

"Blair promised John Howard he would do it during a visit to Australia," says Christopher Price, himself a former Labour MP. "That shows that where there's a will, there's a way." Price insists that the select committee's inquiry offers an opportunity for Labour members to put "real pressure" on the government to come up with a co-operative solution to the Greek marbles.

"If they can do it with bones, then they can do it with stones," he says. "The pressure on Britain to co-operate on this issue is mounting, and it's going to become irresistible when the New Acropolis Museum opens."