Monte Testaccio is a hundred-foot high, kilometre-round pile of broken potsherds. The great mound of ceramic refuse, started in the first century BCE, was added to daily over the following four centuries. Co-existent with the Roman Empire, it grew into a mass whose sheer bulk and consistency could not be reduced. Unlike the empire, it did not fall. Pottery is an especially obdurate artefact, but every single piece of pottery in Monte Testaccio is of a particular sort: each fragment is a sherd of broken oil amphora.

Perhaps Rome’s greatest invention was concrete. Everything went into it: lime and volcanic ash, chunks of rock, brick rubble, and lots of broken pottery – everything except oil amphorae. Lime mixed with olive oil produces a soapy substance, and the Romans took steps to avoid aqueducts full of washing-up suds, temples with slippery steps, city gates foaming at the mouth, bubble-bath amphitheatres. Like concrete, the empire was an amalgam of ingredients gathered from many different sources and bonded together. Just as concrete could be stronger than rock, so the combination of racial and cultural elements made the empire seem indestructible. Monte Testaccio, however, was a monument to non-integration. The makers of the empire kept all the broken bits of oil amphorae away from their recycling centres. When the imperial bonding agent passed its sell-by date and fell apart, Monte Testaccio held together.

Earlier this year, I tried to find a way up it. A modern flight of steps has been constructed on the north-east corner, but it lay behind a locked gate with a ‘vietato accesso’ sign attached to it. In the 1930s the mound was dressed up as a park but it has been mostly closed since the Second World War, partly to protect it but also because the refuse of ancient commerce began to acquire an extra crust of debris from the modern heroin trade. A group known as ‘Eighth Hill’ are pressing the Italian government for open access.

Entry denied, the connoisseur of history’s leavings doesn’t give up without a struggle. Eighth Hill addicts need their fix, partly because the leavings in question hand down from ancient to modern fingertips the physical record of something still in daily use; something we know the feel of, the savour of – its density, rate of flow and soapiness are all thoroughly familiar. We still import it, or much of it, from the same place that supplied the bulk of the oil inside the Testaccio amphorae: Andalucia, which the Romans called Baetica.

Olive oil consumption under the empire has been estimated at twenty litres per person per year. In a city of one million, that makes for a lot of empty jars, but it also makes clear the centrality of olive oil to Roman existence. As D.J. Mattingly put it in the Journal of Roman Archaeology in 1988, ‘the olive was (and is) fundamental in shaping the landscape, the way of life, the economy and the mentality of the Mediterranean.’ That parenthetical ‘is’ now stretches beyond the Mediterranean, since even the present-day inhabitants of Ultima Thule are now within the same – dare I say it – common market.

Olive oil lubricates a set of connections that have been in motion since literate culture began in Europe. The Odyssey is among other things a tale of Mediterranean island-hopping. Britain’s island status may bring it closer and make it more susceptible to this European paradigm than the mainland culture of much of Europe.

In Facing the Ocean (2001), Barry Cunliffe argues that Neolithic and Bronze Age civilisations crested the sea-lanes and that coastal communities were key in the relay of artefacts and ideas. Nowadays, the same routes are escape-corridors for those desperate to flee barbarism. The seas bring peril, but also hope. The land is ring-fenced, unyielding, unmoved.

The Eighth Hill looks down on the Protestant Cemetery, where the remains of Keats and Shelley are buried. The latter wrote that ‘it might make one in love with death, to think that one should be buried in so sweet a place,’ though this was half a century before Testaccio morphed into the Roman Smithfield, lapped by the sounds and smells of industrial butchery. The nearby new Museum of Contemporary Art is housed in an old slaughterhouse.

The hill is now surrounded by bars and nightclubs with names like Alibi, Radio Londra, Jungle Club, Orpheus, On the Rocks, cheek-by-jowl with butchers (still) and copy-shops. Thomas Hardy thought up a poem nearby, one of several written in Rome in 1887, on the shape-shifting nature of time and the collapsing of the present and past into one. Despite the perdurability of its ruins, he thought nothing in Rome really lasts compared to the ‘matchless singing’ of the poets. Hardy couldn’t have imagined the unmatched volume of Testaccio’s nightclub music when darkness falls. The racket fills the air like a sonic pile-driver, pumping noise pollutants into the voids and cavities in the thousands of layers of smashed amphorae, so that every part of the hill vibrates.

All around the perimeter of the hill, the amphora shards are stacked neatly in a series of terraces. Even rubbish was an engineering project. On the surface at least. The interior of the heap was a morass, into which an unending landslip of ceramic trash was released. Like the built structure of the empire, the spectacle of order was a repeat performance, but everything behind the façade was subject to continuous structural change. At a certain point, the most recent arrivals proved in some way anomalous, refractory, inimical, to a degree that threatened the integrity of the whole, and the aggregates of empire and Testaccio both stopped growing. The Empire went into panic reverse mode, recalling the troops and abandoning the edgelands: Britain went its own way in 410, Spain in 472.

On 25 March, EU leaders met to mark the 60th anniversary of the signing of the Treaty of Rome in 1957. The birthday party for the launching of the EU was something of a shipwreck. The 27 leaders pronounced that ‘our union is undivided and indivisible’, despite the absence of the soon-to-depart 28th member, and not so indivisible that they did not also call for ‘even greater unity and solidarity amongst us’. While they fiddled, Rome flared up all over the place. A buffer zone was set up around the Capitoline Hill while the anniversary talks were underway. Apart from the five authorised demonstrations, there were also flashpoints involving trade unionists and anarchists on the left, and groups such as Forza Nuova, Roma ai Romani and Fratelli d’Italia on the right.

Two days later, on 27 March, the police announced the discovery of an enormous illegal toxic waste dump filling a quarry in Aprilia, a few miles south of Rome. I wonder if a Monte Aprilia would say as much about our own economy and culture as Monte Testaccio does about the Roman Empire. The one would be no less international than the other; and if there were a British section, it would consist of fertiliser, nitrogen compounds, plastics, pharmaceuticals, synthetic rubber, petrol, gas and cars – the UK’s main exports to Italy. Even more toxic would be the non-degradable excess of Brexit propaganda, the hundred-feet high, kilometre-round pile of broken promises. And sitting on top would be a still-quivering set of great yellow donkey teeth that once belonged to some forgotten demagogue. Let's imagine that analysis of the teeth to determine the levels of oxygen and strontium isotopes wouldn’t give a clear indication of geographical origin, given Europe-wide patterns of trade and consumption. Our diet doesn’t have a passport. You are what you eat.