Heinrich Schliemann had always hoped he’d find Homer’s Troy. Although he had no archaeological background to speak of, he did have money, and spades, and in the 1870s this would do. Tipped off as to the probable location of the ancient citadel — beneath Hisarlik on the west coast of modern Turkey — the Prussian businessman got zealously to work, pushing through the soil until he struck what he assumed to be the treasure of King Priam himself.

In the Iliad the Trojan king lived lavishly. His palace was ‘surpassingly beautiful’. Its 50 rooms were built of ‘polished stone’. The terracotta wares Schliemann lifted from the ground did not quite evoke such splendour. There were fat-bellied pots with nipples and navels and rustic two-handled cups. They were clearly ancient. As was the gorgeous gold diadem in which Schliemann famously dressed his wife. But as he later realised, much of what he’d found was too ancient, dating to around a millennium before the Late Bronze Age, when Homer’s epics are set. Eager Schliemann had dug too deep.

A cross-section of the ancient mound is recreated at the centre of the British Museum’s dazzling new exhibition, which opens next week. The oldest finds are displayed at the bottom. The richest are far higher up on shelves representing the layer known to archaeologists as Troy VII. If Homer’s Troy was to be found, it was here, in the earth Schliemann rummaged through in his race to reach the bottom.

This exhibition doesn’t come down on one side or the other in the great debate over the reality of the Trojan war. The explorations of Schliemann and the archaeologists who anticipated him in locating ancient Troy at Hisarlik (widely now agreed to be the right spot) are dealt with separately from the stories of Achilles and Odysseus. By the time you’ve worked your way through all the artefacts, however, you’ll have made up your own mind, which is of course the idea.

For those of us who believe that some kind of Trojan war took place, the discovery of arrowheads and evidence of ancient fire in the seventh level of the mound is utterly tantalising. Hisarlik appears to have burned around 1180 BC. An ancient mathematician dated the Trojan war to 1184/3 BC. Did powerful armies make war on Troy and burn the citadel to the ground? It seems possible.

The story begins with Helen and the judgment of Paris. Boarding the boat to Troy in one ancient wall painting, the beauty looks as though she might turn back at any moment. There’s a look in her eyes that says: this can’t be happening. In Homer she bears much of the blame for the Trojan war but, to this artist, who painted her in first-century Pompeii, it was obvious that she never wanted to go.

Many have rightly tried to absolve the ‘evil-scheming bitch’ of the Iliad of responsibility for the war. Artists here present her for what she was: a pawn, a plaything of the gods, a victim of events beyond her control. Sitting forlornly beneath a tree in Eleanor Antin’s kitsch recreation of the scene from 2007, Helen waits for thicko Paris to make up his mind. Machine gun-toting Athena and Hera with her hoover and pinny stand no chance. Aphrodite the vamp will take the apple. Paris will take Helen as a gift from Aphrodite.

When the Flemish artist Hans Eworth came to paint the Judgment in 1569 he dispensed with Helen altogether. Adopting the role of the foppish Trojan prince, Queen Elizabeth I stands at the left of the canvas cradling an apple of her own — a golden orb — before the three goddesses. She is capable and confident and refuses to hand the bauble over. Had Paris only done the same there might never have been a war.

The terror unleashed on Troy by Helen’s husband, King Menelaus of Sparta, and his brother, Agamemnon, King of Mycenae, obsessed ancient Greek artists, especially the vase painters. They showed the Trojan prince Hector bidding farewell to his wife and baby son as he prepared for battle; their boy Astyanax being thrown from the walls; blood spurting from the neck of Polyxena, the youngest daughter of Priam, as she is slaughtered over an altar (or Achilles’ tomb) by a son of Achilles.

While the Greeks were destined to prevail over the Trojans, they endured their fair share of misery, as Homer was careful to show. A magnificent ancient sarcophagus normally housed at Woburn Abbey celebrates the life of Achilles. But it’s the scene in which the corpse of his closest friend (and maybe lover) Patroclus is carried in that is the most arresting. The young man, killed by Hector on the battlefield, rests on the shoulders of a comrade, his head pitifully slumped.

In the Iliad, this episode leads Achilles to return to battle after his withdrawal from the front line. He avenges Patroclus’s death by killing Hector and dragging his body brutally behind his chariot. On a rare silver cup found in Denmark, Priam kneels before Achilles and kisses his hand in the hope of retrieving his son’s body. The scene, one of the most poignant in the poem, unites the enemies in grief. It is staggering to see it expressed on a first-century BC cup with an almost Victorian majesty.

The workmanship of these ancient pieces is rarely less than outstanding. Without sticking rigidly to the texts, the artists treated the Troy myths with the kind of reverence that would later be reserved for Bible scenes. They even succeeded in drawing out their humour — quite a feat — having discovered that Odysseus’s adventures provided particular scope for playfulness.

In Homer’s Odyssey, the so-called man ‘of many ways’ wanders for ten years after the war, desperate to reach his home on Ithaca. It is his misfortune to suffer a string of unimaginable setbacks. The monstrous Cyclops seals him in his cave and eats his friends. Odysseus comes up with a plan. An adorably small Greek bronze of the warrior clinging to the tummy of a ram celebrates his great escape. The big man has shrunk to the size of a sheep.

More popular with artists was his encounter with the Sirens. The Etruscans had them perched alluringly on their stalls with lyres in their hands. Herbert Draper, in his much-reproduced oil painting of 1909, depicted them emerging naked from the sea and sliding aboard Odysseus’s ship like hungry white sharks. Strapped to the mast, Odysseus strains to hear their dangerous song. His men row valiantly on.

Odysseus, perhaps more than any other figure, learned how bittersweet was the Greek victory. The mastermind behind the Trojan Horse, he stormed Troy, only to witness the deaths of his surviving men on his journey home. To escape Troy was not to flourish but to relive its agonies perpetually. It was the genius of Homer to show that there are no true winners in war. It was the genius of the artists who came after him to find the truths inherent in his epics. As Lesley Fitton, co-curator of the exhibition says: ‘The real truth of Troy lies in the story.’