Babylon: Myth and Reality, British Museum, London

The evening before I went to see Babylon: Myth and Reality, I watched Josh Brolin whine and shamble heroically through his title role in Oliver Stone's W. As a double-feature, the pairing makes a sort of sense.

"If you break it, you own it," we hear in W, as the White House neo-cons plan their quick-and-dirty strike. Well, as the final section of Babylon proves with melancholy restraint, the "coalition of the willing" soon owned the site of the ancient city. And they broke it. Alongside images of the military camp and armoured-vehicle park that in 2004 left "a trail of destruction and contamination" among the hallowed ruins (75 miles south of Baghdad), John Curtis – the British Museum's Middle Eastern chief – denounces the "inexcusable" vandalism of coalition forces. These days, only Dick Cheney might object. Would the BM have dared to sound as forthright just after the war?

The Iraq fiasco haunts every room. From 3,000 years of ancient Meso-potamian history, this show opts to focus on the reign of Nebuchadnezzar II (605-562BC) and its cata-strophic aftermath. The conqueror of Jerusalem (twice, in 597 and 587) who deported the Jews into "Babylonian captivity", the king left an overstretched domain that within a couple of decades had fallen almost without a fight into the hands of the Persian ruler, Cyrus II. One of the many Biblical and literary fables of hubris and nemesis that later stuck to Nebuchadnezzar was the idea that, disgraced, he went mad in the desert and acted like a wild beast. William Blake's 1805 print best captures his plight. It's impossible to view it in this context and not think of hairy Saddam on the run, hunted down in his cave.

This underlying anxiety about Babylon and Iraq today might help explain why the "myth" side seems to crowd out the "reality". Yes, the artefacts do awe and intrigue, though for every grand lion or serpent in glowing glazed brick from the city's processional way there are a dozen clay tablets or cylinders inscribed in cuneiform. These baked nuggets of the remote past tell us everything, from the maths drills that tested trainee architects – those giant ziggurats, gates and temples demanded virtuoso precision – to the values of respect for a subdued people, in the post-invasion "Cyrus cylinder". An exhibition with the courage of its convictions would have mounted it next to Col Tim Collins's eve-of-battle speech.

Thanks to a soundtrack, sometimes the tablets speak to us of kings, dreams and battles. This mid-sized exhibition never claims blockbuster status. So the great intellectual adventures that led to our detailed knowledge of life in Babylon – the excavations by Robert Koldewey in the 1900s, or the decipherment of cuneiform by Henry Rawlinson – get slightly short shrift in these displays. Frustrated visitors might want to invest in the superb book, edited by Irving Finkel and Michael Seymour. It fills in the gaps.

Sin and doom hogs the limelight. Whether this works depends on the standard of "legacy" material. We get drippy Victorian paintings of the Jewish exile, while Rembrandt's Belshazzar's Feast has not made it up the road from the National Gallery. A collection of music inspired by Babylon, from Verdi's Nabucco through the inevitable Bob Marley and down to Boney M, looks like the fruit of a Google trawl. Modern art prompted by images of the Tower of Babel – especially by Pieter Bruegel's crumbling helter-skelter – shines brighter, in the eerie digital city of Julee Holcombe's Babel Revisited or MC Escher's never-to-be-finished skyscraper.

Again, I wanted a show that invites analogies between ancient and modern to go the whole Babylonian hog. Burning and collapsing towers, a panic-stricken city, rumours of a vile oriental despot: this show's processional way leads the mind inexorably back to Saddam and Bush.

British Museum until 15 Mar 2009