A pair of square plastic tents has been set up in the British Museum's conservation laboratory. Under one is a fragment of The Egyptian Book of the Dead, under the second an elaborate Torres Strait headdress made of wood, cowrie shell and white feathers. Impressive artefacts, the pair of them. But I am here in this nondescript building at the edge of the City of London to see something else, a collection of fragile carved fragments of ivory, small enough to fit into your palm.

One piece depicts a pair of crossed lions. Another shows a woman, a courtesan perhaps, stripped to the waist, and standing among stylised trees. There is a bird that could be a peacock. Unseen for almost two decades, all were inlays once set into furniture dating from the 1st century, left in a bricked-up palace storehouse not far from the modern Afghan town of Bagram, about 80 miles north of Kabul.

If Bagram, with its huge American airbase, is these days more familiar for its association with conflict, the story of these fragments, too, is a story about war – about wars, indeed. They are mute witnesses to how protracted and corrosive violence, like that which has enveloped Afghanistan for three decades, destroys and disperses the physical evidence of a country's historical culture and threatens to wipe the slate of memory clean.

But they are about something more profound as well, summed up by the motto of the National Museum in Kabul: "A nation stays alive when its culture stays alive." They are testament to how memory and culture persist and survive against even the longest odds and in their survival defy what conflict does.

If proof of that is required then it is demonstrated in the Kabul museum's own history. When I first visited, a few weeks after the fall of the Taliban in December 2001, the building was in ruins, its windows blown out by rocket fire, its floors strewn with rubble and garbage. Since 2004, it has functioned as a museum once again, following a $350,000 refurbishment programme.

These ivories, destined to return to Kabul, not only vindicate the museum's motto, but their presence in the British Museum's laboratory is the result of a remarkable mystery whose details even now cannot be fully told. Stolen in 1992 from Kabul at the height of the Afghan civil war which followed the Soviet departure, these pieces were only finally recovered last year following the intervention of officials from the British Museum with their then owner, who was persuaded to return them.

There is no way of escaping how these Indian ivories from the Begram Hoard, an extraordinary, 1st-century trove – named with the old spelling of the town – that demonstrates Afghanistan's trade connections to the far east and the Roman world, are artefacts whose history has been defined by conflict.

French archaeologists Joseph and Ria Hackin, who excavated the ivories between 1937 and 1939, were killed fighting for the Free French Forces in 1941, leaving their interpretation of the objects unfinished. They were last exhibited in 1978 before the closure of the National Museum in the year prior to the Soviet invasion, and disappeared at the height of the fighting in the internecine war that followed the Soviet withdrawal. When they are returned, it will be to a country still at war.

In the London laboratory, conservator Barbara Wills is working on a dozen or so of the ivory and bone inlays. They appear, at first sight, to be complete objects, once broken and then reassembled into coherent wholes from the pieces the Hackins and their collaborators found. Wills turns one over, a figure of a woman, to show the grain of the ivory and how inappropriate fragments stuck in during their first reconstruction, while making sense of once-existing holes, had come from other pieces. One of her colleagues shows another piece depicting a lion. A sliver has been removed from where an earlier conservator had glued a piece in the wrong place so that it now makes sense.

On her table, Wills has resin and a paintbox to colour small sections that she has filled to strengthen the ivories. Sometimes, however, it has been a question of removing the old adhesive from earlier attempts to stick the ivories together.

"This has been reconstructed," she says. "You can see four or more episodes of damage. The last probably happened while it was in the Kabul museum." She picks up another of the delicate pieces and rests it on her blue glove. "You see this as one object. But when it is examined, it has potentially parts of three objects in it."

This is not the only problem to have been caused by older conservation efforts, Wills explains. When the French team discovered the buried storerooms containing the Begram Hoard, the ivories were shattered and in a state of poor preservation. To lift the fragments without disturbing them, Jean Carl, one of the French excavators, devised a new technique, pouring warm gelatin on to the pieces to allow them to be lifted. The problem with the gelatin, Wills says, is that in the subsequent decades it has contracted and threatens to pull off the surface layer.

What is not visible to the naked eye is how the ivories must have once looked when they were attached with metal pins to long-rotted chairs and footstools. Using a special spectroscopic technique and x-ray fluorescence analysis, scientists at the British Museum have identified four different types of pigment once used to colour the pieces: red, dark blue and two types of black, suggesting that the inlays were once painted in vivid colours long since faded.

The museum's conservation efforts, as head of the department, David Saunders, explains, have an important purpose to ensure that when the ivories are sent back to Kabul they will be better equipped to last. "We don't want to send back three loose pieces."

The fact they will be sent back at all is part of the incredible story of these objects – because the ivories were stolen and kept hidden for almost 20 years. In the preface to a booklet that accompanies what will be the ivories' first public showing outside Afghanistan, British Museum director Neil MacGregor alludes to the miracle that brought these ivories back to light. "Exported and sold illicitly on the black market in antiquities," he writes, "thanks to a great act of generosity, they will now return to Kabul." The vagueness is deliberate because of the sensitivity surrounding their return.

St John Simpson, a keeper in the Middle East department at the museum, fills in some of the blanks. "These pieces were very well known. But between 1992 and 1994, the National Museum in Kabul, where they were kept, was repeatedly looted. During this period of civil war, they were stolen. Their whereabouts was completely unknown. We did not know if they had even survived."

Renewed interest in recovering the ivories was stoked by the success of the exhibition Afghanistan: Crossroads of the Ancient World, which has toured six cities in the US, Canada and Germany before its arrival at the British Museum next month. It is in the London leg that the ivory inlays will go back on show for the first time.

"With all the publicity surrounding the travelling exhibition, the ivories were back on the radar," says Simpson. "We were approached by various parties last year to see if we could get them back. We were advised that they had entered the UK and were in private hands – I can't speculate about motives – but we were told it might be possible to 'receive' them."

There is considerable caution in the way Simpson describes the efforts to recover the pieces, not least because whoever had them must have known they were stolen. Indeed, in the decades since they disappeared, the ivories have been included on Unesco's watch list of missing artefacts, a fact no legitimate museum, collector or dealer could have been unaware of.

"It was the director of the National Museum who had an understanding that they were here in the UK. The owner knew they belonged to the museum in Kabul," says Simpson. "You know there were individuals who held objects from the museum in good faith to protect them during the Taliban period, so I can't speculate why the owner of these ivories returned them or what pressure might have been applied."

Their recovery, however, speaks of another, longer mystery, less elusive in the way it has unravelled: precisely what these objects have to say about Afghanistan's culture 1,900 years ago.

It was not the French who first discovered the ancient city of Begram, but the 19th-century English explorer Charles Masson, who believed he had discovered one of the cities established by Alexander the Great as he progressed through Asia – Alexandria ad Caucasum, set close to a pair of strategic mountain passes linking Bactria with northern Pakistan.

While Masson collected coins and minor antiquities, it would not be until a century later, when the French signed a treaty giving them a monopoly on archeological exploration in Afghanistan, that the city would be properly excavated, starting in the 1920s. Alfred Foucher, one of the first to dig, was unconvinced by Masson's claim. Instead, he proposed that the city was Kapisa, the summer capital of the Kushan kings, who ruled a state stretching from northern India to Afghanistan between the 1st and 4th centuries AD. By the 1930s, another group of French archeologists was working at the site, first, Jean Carl and Jacques Meunié, and later the Hackins. Naming their site the "New Royal City", it was in 1937 that two bricked-up strongrooms were found, containing large amounts of bronze, alabaster, Roman glass and ivory, even Chinese lacquer.

Located on the ancient Silk Road, academics have long debated the meaning of the site and the discoveries found. For a long period, it was believed the storerooms represented a royal treasure that had been hoarded by the Kushan kings in a series of treasure houses. But more recent studies have suggested that as many of the objects can be dated to the 1st century AD, far from being the hoard of kings, the storerooms were commercial warehousing for luxury goods travelling the Silk Road. This would explain the diversity of the objects found.

The ivory inlays, says Simpson, were almost certainly manufactured in India and fitted into furniture that they decorated there. "What does this tell us about Afghanistan in this period? It was a multicultural society which included wealthy individuals fully comfortable with exotic influences." Echoing the ivories' history during Afghanistan's recent conflicts, Simpson believes it is possible that the storerooms may have been walled up in the first place because the area was then going through a period of "instability".

"Culture is a fragile commodity. There are so many different factors in why a lot of cultural objects do not survive. The conditions of burial are against survival, especially cloth and wood. There is also the tendency – in ancient societies as well as modern – to recycle, particularly where the resource in question is limited and very valuable, like metal.

"Why these pieces have survived at all is because the officials at the museum took the very wise decision to remove the objects from the display cases and move them into storage. You have to remember that the museum itself was hit by a rocket. No one could have guessed how long the war would go on or what would happen to the storage facilities or the museum."

The exhibition, Afghanistan: Crossroads of the Ancient World, is at the British Museum, 3 March-3 July 2011. Further information at www.britishmuseum.org