Medals are usually awarded for something done well. In sport, in war, for society. So the notion that they might also reward bad behaviour is counterintuitive and provocative. Artists, however, being counterintuitive and provocative so-and-sos, have approached the whole medals thing with laudable independence. And a feisty historical show at the British Museum ignores the dull and predictable territory of the gong of honour in order to investigate the unpredictable and downright naughty terrain of the gong of dishonour.

Since at least 1588, and probably earlier, there has existed a breed of artistic medal-maker whose ambition is not to glorify or to praise, but to mock, insult, accuse, abuse, undermine, demean and generally take the piss. The earliest example here is a Dutch roundel, dating from the reign of Elizabeth I, that celebrates the sinking of the Spanish Armada by the English fleet. The Dutch supported the English as Protestant brothers and because they were fighting their own war of independence against Spain. At the top of the medal — which shows the Spanish navy capsizing, Captain Pugwash-style, in the English Channel — the artist has added the legend and date “Veni, Vidi, Vivi, 1588”, a sarcastic misquotation of Caesar’s famous “I came, I saw, I conquered”.

So it’s an immensely childish object. The ya-boo-sucks tone adopted by this medallist is the tone of the playground or the partisan daily cartoon. Half a millennium after the historical events depicted here, I can easily imagine a stand-up at the Comedy Store adopting more or less the same tone to make more or less the same point.

This refusal of the medal of dishonour to mature or to date is what I found most amazing about the entire display. On the honourable side of the medal equation — in politics, in religion, in education, in language, in sport, in science — humanity has changed beyond recognition since 1588. Its every thought has progressed.

On the dishonourable side, however, it seems not to have altered a jot, and remains as doggedly puerile as ever.

See, for instance, what is being done to Louis XIV in another Dutch medal, produced a century later in 1689. At one of the great French royal’s exposed ends, the pope is giving him an enema with what looks like a rolling pin. At the other, he is being forced to vomit all his money into a chamber pot! The Dutch medallist who did this to Louis was angered by the burning of Koblenz by French troops. The French, it seems, had pioneered the ruthless bombardment of cities, a type of urban warfare in which large numbers of civilian casualties were unavoidable. Evil is being attacked with scatology.

In response to this excellent observation that human childishness is immune to genetic change, the British Museum’s show is split handily into two self-contained chunks. The first concertinas 500 years of medal history into a tight display dealing with all the medals struck before the second world war, while the next luxuriates in the energetic cynicism displayed since then by the modern artist. Rounding off the event are some brand-new medals commissioned specially for this show by the British Museum from well-known contemporary trouble-makers. Thus, instead of Louis XIV’s enema, we have the Hutton Award, given to Tony Blair and Alastair Campbell for taking us into Iraq, by the great Richard Hamilton; and a special commemoration of the English hooligan Dean Rowbotham, “for breaking his Asbo on more than 20 occasions”, struck by Michael Landy.

Before we plunge fully into the delights of this miniature bronze edition of Mock the Week, however, we should ponder for a moment the general plight of the medal. Whether they honour or dishonour, medals are fiendishly awkward objects to savour. No bigger, as a rule, than a bottle-top, they are difficult to view and well nigh impossible to read. The British Museum has an incomparable collection of them, and determined saddos like me have learnt to press our noses against the protective glass, strain our eyes, consult our encyclopedias, and managed, despite the odds, to admire them. Still, they are an acquired taste.

So this exhibition ought to have tried harder to make them viewable. How annoying to read that The Bombardment of the French Coast of 1694, by Christian Wermuth, shows a French cock being emasculated by an English mouse without being able to witness the event — because it is on the back of the coin. These curators should visit the Wallace Collection, where they will learn how to do useful things with magnifying glasses and mirrors.

Although the tininess of the medal results in serious viewing problems for the spectator, it leads also to great inventiveness and some superbly concentrated rudeness. The three chappies having a collective poo in Wermuth’s vicious pictorial complaint about the Peace of Utrecht, from 1713, represent Britain, France and Holland, who had signed an agreement not to fight each other. The German medallist insists this is temporary. On the other side of the coin, he duly shows the three of them a year later, throwing their poo at each others. Topping off the action is a scatological pun in Latin, “Pax in trec”, which reads like “Peace in Utrecht”, but means “Peace in excrement”.

This instinctive mockery comes naturally to the early medallists in the show, but is more forced among recent exhibitors. David Smith, that fine American abstract expressionist, makes an ambitious but clunky effort to satirise the dark state of the world in 1939. Packed with allusions, his busy medals require too much detailed reading of too many footnotes. No such problems with Marcel Duchamp’s hilarious Sink Stopper medal, released in 1967. All he has done is cast the plug from the sink in his holiday home in silver — the result addresses the ultimate worthlessness of all gongs.

I also thought the Chapman Brothers, in a rare failure, had made a similar mistake to Smith’s by producing a medal too crudely crowded with skulls, skeletons, Nazis and dead bodies. But I underestimated their wickedness. Stepping back, you suddenly notice that the busy clusters of corpses actually form an obscenely grinning smiley badge. In the doomy chorus of the medallist’s global lament, the most effective sound remains the cackle of the clown.

Medals of Dishonour, British Museum, WC1, until September 27

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