The British Museum has always been a fabulous resource. Look what it owns. Not even the line-up of seven dwarfs who preceded St Neil MacGregor in the director’s chair could seriously damage the clout and width of this magnificent hoard of global treasures. Yes, much of it was stolen or inveigled from its rightful owners. (But when it comes to the acquisition of great art nobody, ever, has been entirely innocent.) Yet for all the splendour of its ill-gotten gains, the BM has had considerable difficulty finding a proper niche for itself in the modern museum world. “How to be relevant?” must echo around these splendid chambers nightly once the lights are switched off.

It is a great collection, but what is its greater purpose?

Earlier directors were too small of mind and stature to worry about it. But St Neil is a museum figure sent down to earth by God precisely to sort out stuff such as this. He would have realised that the colonial age was over, and that vacuuming up other people’s international goodies was no longer enough of a role: the BM needed a higher function. So he has given it one. Subtly, cleverly, MacGregor has turned the BM into a spectacular teaching aid that allows us to understand the present better by looking more closely at the past.

The Sudan show here in 2004 illuminated the Darfur conflict more vividly than any number of reports on News at Ten. The First Emperor exhibition that wowed so many visitors had so much to tell us about China at a time when knowing about China was crucial. And now Hadrian has arrived.

Most of us know one thing about Hadrian: he built the wall that crosses the north of England. After that, his achievements blur. But the overall message of the historical mega-biogs the BM has taken to mounting is that one man can change the world. The First Emperor did it. Hadrian did it. Karl Marx, who wrote Das Kapital in these same rooms, did it.

When Hadrian ascended to the laurel in AD117, the Roman empire was in turmoil. His predecessor, Trajan, had overextended the imperial reach and uprisings at the edges of Rome’s holdings were threatening stability. Mesopotamia was revolting. Judea was exploding. Macedonia was bristling. And another rebellion had broken out in the troublesome province of Britannia. In other words, there was trouble in Iraq, Israel, the Balkans and here. Had Fiona Bruce been reading the news in Hadrian’s day, she would have been lamenting pretty much what she laments today.

Hadrian’s first meaningful act as emperor was to retreat from Mesopotamia — to pull the troops out of Iraq — thereby ridding the empire of a distant problem it didn’t need. In Judea, he ruthlessly put down the Jewish uprising and gave the province a new name: Palaestina. In Britain, he built a wall that marked the outer limits of the empire and symbolically separated Englishness from Scottishness, thereby creating a divide to which we seem to be returning.

All this the show tells us with an exemplary mix of maps, models, mementos and masterpieces. The BM’s storytelling skills have sharpened considerably since St Neil took over, and the brutal thematic clarity here is worthy of Hadrian himself. To prove how up-to-the-minute history can be, the opening object is a colossal head of Hadrian discovered in Turkey only last August. It shows him to have been the first emperor to sport a beard, perhaps to cover up some facial blemishes. With his fleshy cheeks and unruly mop of curls, Hadrian looked uncannily like a white marble Rory McGrath.

He was actually Spanish. And grew up in modern Andalusia in a privileged community of wealthy landowners who had made their fortunes supplying Rome with olive oil. A row of dusty amphoras stamped with Spanish initials seeks successfully to evoke the quotidian nature of these Iberian origins. The burial tablet of the wet nurse who brought him up adds another humanising touch. And we learn that Hadrian had an unusual crease across the top of his ear lobe, which features in all the authentic busts of him. It was probably caused by genetically inherited cardiac problems, and has proved an excellent tell in the hunt for fakes. Those of us who had always imagined that Roman portraiture was concerned solely with mass-producing the official image and never with the search for individual likenesses will have to re-examine our position.

Hadrian’s accomplishments as a war leader are darkly impressive. Having withdrawn from Mesopotamia, he was free to squash every hint of rebellion nearer home. His behaviour in Judea was outrageous. One contemporary report claims that 580,000 rebels were killed. A few precious possessions left behind by fleeing Jews in AD132 were rescued from a cave in a desert wadi and are now on show here, perfectly preserved. The rope attached to a gorgeous bronze bowl might have been knotted in Jerusalem yesterday.

Hadrian as warlord appears most memorably in a whopping great statue in full armour — imagine the Incredible Hulk in Bacofoil — in which he stamps on a tiny retreating scaredy-cat, probably a rebellious Jew. Can this really be the same Hadrian whose achievements as an international builder have left us so many monuments to admire in so many countries?

In AD122, he arrived in Britain to see for himself what was causing the constant bellicosity of the tribes and to initiate the building of his famous wall. When I was at school, Hadrian’s wall was explained as the last line of Roman defence against the invading Scots. It now seems that it was built to clarify the empire’s northern edges and to make easier the collection of taxes and suchlike. Everywhere Hadrian went, he built. But his finest construction achievement was surely in Rome itself, where his glorious Pantheon still stands, and is the model for every substantial dome that has followed it. The Castel Sant’ Angelo is still there too, originally built as Hadrian’s mausoleum; and outside Rome, in Tivoli, the fabulous villa complex he dreamt up remains as well in substantial fragments. What a legacy.

Hadrian the builder and Hadrian the war beast are joined by the third main imperial identity identified here: Hadrian the homosexual. Tales of his devotion to his Greek lover, Antinous, have come down to us in various nudgy and winky forms, and much is made in the show of the open-mindedness of the Romans in matters of gayness. Antinous, who died in a mysterious river accident in Egypt, was quickly deified by Hadrian and worshipped as a god around the empire. The resulting statues show a beautiful marble Adonis with softly feminine looks.

Yet something about this reading of the situation doesn’t quite ring true. The Hadrian who has hitherto been evoked is surely too clever and ruthless a political manipulator to have allowed his sexual preferences to be given this florid an airing. The public taking of Antinous the Greek as a lover makes more sense as a deliberate political manoeuvre designed to ingratiate himself with the Greek-speakers who still made up 50% of the empire. A gay marriage of political expedience?

Anyway, it’s an exemplary piece of storytelling, achieved with exactly the right mix of telling objects and great art. The show is not, and cannot be, as exotically intoxicating as The First Emperor, but does its job just as well. This franchise could run and run.

Hadrian: Empire and Conflict is at the British Museum, WC1, from Thursday until October 26

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