Saturday came around again. Another ragged, multicoloured column of adolescents passed by under my window, each pulling a suitcase over a sounding board of stone paving chevron-grooved to keep pedestrians upright in slippery conditions.

The roll of assorted valises has spontaneously composed itself into a kind of municipal anthem of twenty-first-century Florence, played incessantly in every street of the centro storico at any hour on any day. Orchestrated by the migratory patterns of global tourism, it is an anthem conferred from outside and constitutes the soundtrack of today's processional routes, the ones established by visitors seeking out the addresses where guidebooks advise they stay.

Main streets and side roads resonate with a monotone concert of baseline rumbling as hard tiny plastic wheels rotate on steel axels low-slung beneath compact baggage. Subtly inflecting this steady low tone are insistent staccato clicks chirruping from contact with the grooves. Above both bounce a purposeful gurgling which adds an unexpected harmony, concentrated in who knows which part of the miracle motion of modern luggage.

Unobtrusive despite its ubiquity, this mechanical muzak insinuates itself into the general bustle of the city, like weaving in a textile. From Santa Maria Novella, where trains and coaches halt at the 1930s railway station, its minimal melody courses along Via de' Cerretani before taking any of three turns to the right: at Via de' Tornabuoni, Via Roma or it holds until after the Duomo to veer off down Via del Procònsolo.

The undertow of clicks and gurgles rumbles into the main arteries of central Florence with inevitable banality. The roads take it without complaint, though, for not only are they well worn, they are ancient hosts of foreign feet. Previous hordes, less good-natured than jet-wearied tourists, have imported their wheeled hardware and marching songs into unwelcoming Florence. The Germans in 1943 came, conquered and blurted 'Horst Wessel' before retreating the following year to the percussive din of the explosives detonated to halt the advancing Allies with fallen historic masonry.

The same routes rang to manoeuvres of Austrians and French in centuries before; to taunts of warring Ghibellines and Guelfs; and to the onrush of rapacious Franks and Goths. We can imagine all approaching their destinations along the same itinerary of thoroughfares, passing buildings that reverberate today with the tickety beat of revolving plastic wheels.

These routes yield uncomplainingly. They have outlived the city's great history, having been laid down when a place auspiciously called Florentia had only recently appeared on the Tuscan plain beside the River Arno. Julius Caesar's name is linked with the soon-to-flourish city's creation. But folklore has a taste for the most august and possibly Octavian deserves more credit for seeing this walled colony planted on drained lowland soil. Tucked inland by a narrow margin, Florentia identified the easiest point around for a ferry to cross the river and put legions, administrators and travellers on the road south to Rome.

Thus Florentia acquired its own roads. Known now as Via de' Cerretani, Via de' Tornabuoni, Via Roma and Via del Procònsolo, each of these prime streets of Florence today was a via principalis of that new point on somebody's map around 41BC. Naturally, the names have changed: the Cerretani and Tornabuoni are relatively recent notables, people of the Middle Ages. In terms of the Classical era, they lived only yesterday.

Via Roma, at least, promises a link with Antiquity. But no Roman dux named it. Instead Il Duce's regime endowed every prominent Italian town in the 1920s with a road citing the capital, an attempt to engender a sense of nationhood in a country, still today, reassuringly but alarmingly incohesive about its identity.

No, those road names ride the shoulders of ancestors that followed the lines of the first city walls. Tornabuoni was the western flank; Procònsolo on the east; and where Cerretani leads away from the Duomo the north wall stood.

So on that Saturday I was thinking of walking the bounds of Roman Florence. Being the weekend, the question was whether to wait until the approaching working week when surely there would be fewer people around. But there are never fewer people around in Florence: there are just escalating grades of 'more'. Have so few roads ever been so incessantly pounded as those in this city centre?

It comes, then, as no surprise that any trace of the Roman past lies a metre beneath today's surface. Venice may be sinking because of global tidal action, but Florence is being pushed down daily, hourly and every minute by the strictly local impact of stiletto, shoe and trainer.

To circumnavigate the Roman city is not a time-consuming objective; by our standards, Classical Florentia did not cover a large area. Nor is it hard to identify the streets because the original gridded plan is discernible today.

But not at street level. Ancient remains are almost unheard of here. One reason is that Florence developed so fast in medieval times that buildings came and went. Another is that Florence is not thought of in terms of Antiquity. The Renaissance is the city's key cultural brand and it is that tier of existence you can see – and it is, admittedly, magnificent.

During centuries of economic and social foment, new streets have climbed, curved and cut paths, narrow and densely built upon, across and over the first geometric street plan. But that Roman urban ancestor left its mark indelibly on the city. And it is visible from two hard-to-get perspectives – from below and from above.

For a glimpse of the original city you need to peer into basements. That of In Piedi Nudi nel Parco, the self-styled 'concept store of avant-garde designers' on Via del Procònsolo, is obligingly visible. The developer of the shop's modern building made the floor of toughened glass so that beneath display mannequins and racks of clothes are illuminated stubby old walls and the circular aperture of a well.

On the adjacent road surface, the past is neither present nor vestigial but is symbolic. Two concentric metal rings sunk into cobbles of indeterminate date mark the circumference of one of the round towers that were a feature of the city wall. The stones have gone, maybe to lay other roads, but the image remains.

That image of history's imprint on the present is most powerfully evident from above. It's best seen from Brunelleschi's cathedral cupola or in the abstract elevation that a map supplies. Holding the centre of the city plan is a rectangle orientated towards the cardinal points on a compass. Beyond and within this hub streets may dawdle, fan and congregate in messy huddles and ordered grids, pointing this way and that. But that Roman enclosure holds.

Criss-crossing the rectangle are the two thoroughfares that connected the four gates within the Roman city. Every Roman town possessed its cardo and its decumanus and where they crossed was the Forum. Florence has not lost these coordinates. Via Roma and Via Calimala follow the same north-south axis, while the Corso and Via degli Strozzi bring the ancient west-east road into the twenty-first century.

At their intersection now sits the arid expanse of Piazza della Repubblica. A warren of vicoli and pocket-sized piazze known as the Jewish quarter was condemned as squalid and razed to accommodate this monument to hubris. Self-consciously designed as the new forum for a Florence briefly, in the 1860s, the capital of a newly unified Italy, it was once fashionable to sit at the café tables of Le Giubbe Rosse and Gilli. The new Italy was hungry for Roman models of greatness.

The cafés still buzz. The talk of leisured boulevardiers joins the cacophony melding street peddlers' calls with the tedious repertoires of gypsy combos, tourists' chatter, the gleeful yelps and rosined-toned hurdy-gurdy notes spiralling from the carousel and, at night, the kitsch crooning that taints the atmosphere around Paszkowski's forecourt: the transient republic of modern Florence.

The southern extent of the Roman centre departed from the strict geometry of the quadrilateral. It remains unclear whether this deviation occurred on account of bad surveying or, more likely, because of the changed rhythm of the ground as it slid across that open margin towards the river. But the echo of these first decisions informed the subsequent growth of roads and palazzi.

For turning out of Via del Procònsolo into Piazza della Signoria, the square over which the Palazzo Vecchio presides, the road climbs a gentle gradient. That slope is probably what remains of the banked rows of seats in a Roman theatre, the semi-circular structure constructed on the edge of town.

The present-day palazzo sits roughly above this theatre and the walled complex of which it was part. The choice of location was not symbolic (maybe to mark out the city's medieval patrician rulers as heirs to Rome) as much as it was practical. The Romans built well and for centuries afterwards offered their successors firm foundations, especially important in land once marshy and still traversed by rivers.

And that thoroughness in construction is why main roads follow the Roman roads and why, a few hundred metres from Via del Procònsolo, a fascinating survival of the classical past reverberates in the minds of pedestrians who grasp the significance of the streetscape's distinctive shape.

West of Santa Croce, across Via dei Benci, a cluster of narrow roads meandera this way and that through small courtyards and beside high-sided buildings that abut the street. Two roads curve quite precisely behind a block that faces the wide piazza in front of the marble-decorated front of the Gothic basilica.

They follow the outline of the Roman period's most recognisable monument, the Amphitheatre or coliseum. Built outside the Roman fortifications, it marked the town's growth eastwards. The Medieval buildings that engulf its site prized the monument's foundations (and, conceivably, abundant materials) and retained its elliptical footprint. The road that echoes its contours continues to acknowledge that predecessor in its name, Via Torta, the 'twisted' road.

Roman Florentia reached this far. As Saturday slipped into late autumnal evening, rainwater was cupped in puddles reflecting street lamps in the miniature hill-and-valley surface of the Florence streets of today.

Our era has a strange relationship with history, compartmentalising the past with thematic ideas about heritage. Preoccupied with the present, impatient for a future that also provokes anxiety in us, we seek tangible contact with earlier epochs that are written about but muddied in perception by the fantasising of film and literature. Maybe the past is already inexhumably buried in our minds. Yet it contains many answers to questions we find ourselves asking about the environment we occupy.

The evidence, after all, is there, resonating underfoot.

Land Observations plays DRILL:LONDON on Friday, March 22nd. Also on the bill are Scanner collaborating with Gazelle Twin, Graham Edvard Lewis and Klara Lewis. Tickets can be found here

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