There are fewer than 20,000 licensed black-cab drivers remaining in London, yet despite the inception of G.P.S. navigation systems, all of them are still exhaustively schooled in the geography of a conurbation so massive, so old, and so storied that its epithets—the Great Wen, the Smoke—conjure up primordial images of a chaotic, infective environment.

How extraordinary it would be to have the cabbies’ learning (or “nous” in Cockney), which consists of not simply knowing the names of every single street and notable building within a six-mile radius of Charing Cross but also how to drive the shortest distance between any two of them.

This “Knowledge,” as it’s gnomically referred to by its adepts, represents such a vast quantity of data that those who’ve, in the parlance, “done it” can be shown via M.R.I. scans to have significantly increased the size of the posterior hippocampus—the area of the brain involved in spatial orientation.

There are many transport options in London, but using your feet is best.

You still see “Knowledge boys”—and a very few “Knowledge girls”—puttering about town on scooters with acrylic map holders mounted on their handlebars, but I doubt they plan their “runs” in the traditional way, which was to get a large-scale, folding, A-Z street map of London, stick a thumbtack in at the starting point and a second at the destination, then wind a length of cotton around them. The task was then to follow the straight line formed on the map as nearly as possible on the ground. This was doing the Knowledge “on the cotton.”

And it’s the principle I’ve decided to adopt when introducing you to the inexhaustible, living palimpsest that is my natal city. It may well be the coincidence of the location of my birthplace, old Charing Cross Hospital, with the navel of the cabbing world that’s made me so very interested in creating my own body of London knowledge.

Its epithets—the Great Wen, the Smoke—conjure up primordial images of a chaotic, infective environment.

In order to give you a soupçon of this nous—hard won from decades of flânerie and promenading—I’ve stretched a length of cotton across an old-style, A-Z folding map of the city and drawn a line diagonally, bisecting a square encompassing the southeast of London’s central district. Dictated only by geometry, this line begins at Pendrell Road, in Lewisham, and ends at Blackfriars Bridge, on the River Thames.

I’ve always pooh-poohed such stratagems as this in the past—drawing a circle round a wineglass placed on a map of Paris, then tracing this on foot in the city’s streets. But the second I drew my own arbitrary line, I could see its explanatory value. I’m always adjuring visitors to London of all kinds to explore the city a little more adventurously and to avoid the most celebrated sites, many of which have become mere commodities under the pressure of mass, globalized tourism.

The real spirit of urbanity, I tell them, is, was, and always will be found in the spaces in between places. Moreover, every somnolent cul-de-sac and sleepy side street comes complete with its own mythos: London really has been talked and thought and written about for that long, by that many.

Terence Stamp pauses from his plodding beside the Thames.

My line cuts through all this yarning—and really, when I consider the matter further, I realize that while I haven’t followed the cotton across my hometown before, I’ve done it in many other cities: walking a straight line across any built-up area. Compelling your attention to what’s in your path, and requiring of you a Knowledgeable level of urban awareness, teaches you more about its geography, human as much as physical, than many weeks spent shuttling about on the Tube or by bus, car, or bike.

Which brings me to Pendrell Road. Cities have their dating rings the way trees do, and our peregrination begins in that circle of our conurbation built loosely in the mid-Victorian period. Yes, yes—it’s true that stricto sensu London is a couple of millennia old, but the Roman settlement only ever consisted of the so-called Square Mile—what’s now the financial district—and a few outlying developments on the south side of the river.

The real spirit of urbanity is, was, and always will be found in the spaces in between places.

Up until around 1830, London extended to no more than the area covered by Zone 1 on the contemporary Tube map—Zone 2 was added 60 years later; 3 and 4, between the World Wars. The actual built environment of the inner city is overwhelmingly Victorian—and if you want to get a good portrayal of this monumental building boom, read the second Sherlock Holmes story, The Sign of the Four, in which our hero hales a growler—a four-wheeled carriage—outside the Lyceum Theatre in Covent Garden that takes him all the way out to a large and mysterious house on Sydenham Hill, seven miles away.

Not far from the start of our walk, which is close to Nunhead Cemetery, there’s an impressive gathering of neoclassical, soot-streaked mausoleums, for the most part tenanted by those who died a couple of decades before the surrounding terraced streets were constructed. This is how cities expand, with the living leapfrogging over the developments of the dead. Rising behind the cemetery is the impressive massif of One Tree Hill. Queen Elizabeth I apparently picnicked here before entering the city after some victory or other. Not that she was actually fighting—but you get the point.

If so, she would have enjoyed the spacious views out over the Thames Basin—but not the long, curving roads terracing the hillside, and lined with the 1930s semi-detached houses so typical of London’s outer burbs. Influenced by the Arts and Crafts Movement of John Ruskin and William Morris, every Englishman and Englishwoman’s little castle in these faubourgs contains features—hung tiling, bulls-eye windows, fake black-and-white beams and plastering—redolent of a Merrie Tudor England that never existed.

Whether you amble or stride, you’ll find that London’s streets, alleyways, and cul-de-sacs are paved with gold.

Resuming our own line, we “comply” Pendrell Road (a marvelous cabbing expression that means to go straight on), turn right onto Pepys Road—named for the celebrated diarist, whose vivid portrayals of 16th-century London include accounts of many walks across it—then go left onto Kitto Road. A mile or so of dodging through the streets of Victorian terraces, with their snot-colored stucco-and-red-brick façades, and you reach Clifton Crescent—a well-restored, gently curving row of impressively sized houses dating from 1846 to 1852.

These were built for upper-middle-class families who had live-in servants and kept carriages: it’s with the inception of regular public-transport services in the latter half of the 19th century that London’s rich took a giant bound, out to the very limits of the built-up area, leaving these sorts of houses first to plunge down-market into multi-occupancy, then, latterly, to be gentrified.

Around the corner is Caroline Gardens, now private dwellings but built as an almshouse in the late 1820s. Just as the city’s music is born of a counterpoint between its dead and its live inhabitants, so is it also one between public and private housing: the almshouses, funded often by charities and professional associations, are the forerunners to the great gray concrete behemoths you’ll encounter to the south of Burgess Park, after a further three-quarters of a mile on the cotton.

If you walk west along the central thoroughfare of the park, you’ll reach a point where an old bridge is marooned over the footpath. This is the “bridge to nowhere”: the park itself was laid out over the Camberwell basin of the Grand Surrey Canal, which was excavated in the early 1800s to carry timber from the riverside docks in Rotherhithe. The park, I think, still feels a little watery—an ambience modulated by the presence, on a sunny summer day, of scores of picnic parties: West Africans cooking pork and jollof rice, Colombians grilling carne arepa, Indians eating from ghee-yellowed Tupperware.

It would be invidious to simply list all these people, as if it were a roll call of diversity—the point is, you won’t see them in their habitat if you don’t venture outside the entertainment and business districts. I make no apology for asking some actual walking of you, and for considerable distances. Cyril Connolly, the English writer, once said no city should be so large that you can’t walk out of it in a morning.

This is how cities expand, with the living leapfrogging over the developments of the dead.

Well, London is considerably larger than this—and it takes a long north-of-the-northern-hemisphere day to reach green fields on foot from the center. I know—I’ve done it several times—but even a modest five-miler such as this route will give you a proper sense of its heft, its topography, and, yes, its genuine diversity.

The frankly scary ziggurat looming over the park from the south is Taplow House, built in the early 1960s as the longest apartment building in Europe. It was constructed using components pre-fabricated elsewhere and then assembled on site, as if Le Corbusier had devised the world’s biggest Ikea flatpack. It is a beast, and sits at the heart of a housing project—or “estate,” as they’re whimsically called in England—called the Aylesbury, of which the great German-born architectural historian of Britain, Nikolaus Pevsner, said, “An exploration can be recommended only for those who enjoy being stunned by the impersonal megalomaniac creations of the mid–20th century.” What’s not to like? So, do just that: much of the estate is accessible by aerial walkways, from which you can spy out your route ahead.

Tom Courtenay tests his “Knowledge” on the London streets in Billy Liar.

East Street, a couple of blocks on, holds a market most days of the week and has done for well over a century. Nowadays, it sells everything from smartphone cards and vapes to salt cod and giant Nigerian bottles of Coca-Cola (as if the classic bottle had been scaled up by a factor of four—they’re truly unheimlich). In Dickens’s time the barrows holding the goods would’ve been lit at night and on dark winter afternoons by naphthalene lanterns. Now it’s L.E.D. fairy lights.

Another quarter-mile and we rejoin our line at Manze’s eel-and-pie house on Tower Bridge Road, one of the few remaining venues for this Cockney fodder. It’s edible Victoriana, and served in it: the interior of the house is all marble and wrought iron—while the fare is delivered unceremoniously at the counter.

A ladle of jellied or stewed eels (watch out for bones), a spoon of mashed potato, and a ladle of “liquor,” an odd sort of pea juice. You might want to try one of the pies as well: dry, unleavened pastry with a meat filling that could do with a DNA test. Be brave and do it—and if you find the flavors and textures indescribably strange, wash them down with large drafts of dandelion and burdock, an equally atavistic soda.

You should eat here, rather than at Borough Market, which falls not far from our line: at this old covered market, an international league of posturing gastronomes cram into the storied structures, intent on olive oil so virginal it’s immaculate, and all manner of other comestibles that, while of great quality and profusion, are also stratospherically expensive.

Over it all looms the flint-knapped tower of the 13th-century Southwark Cathedral and, beyond it, the glassy empyrean formed by the new superstructures in the financial district of the city, on the north bank of the river.

I was intending to take you farther, via our unreeling line across London, to where it crosses the Thames beyond the Tate Modern art gallery. But the sad fact of the matter is, I’ve run out of available space the way London cabbies, arguably, have run out of road.

But don’t worry: walk down Bank End from Borough Market, and then along the river walkway and under Blackfriars Bridge. Just past the bridge, you’ll see a place where it’s easy enough, with a little scrambling, to get down onto the river’s foreshore beneath the embankment, which at low tide is fairly extensive.

Two-wheeled travel is discouraged, unless you’re Jane Birkin and Ray Brooks in The Knack … and How to Get It.

I like to sit down here and watch Old Father Thames tossing restlessly in his bed as he roils toward the sea, some 30 miles distant. I love these intersections between human and physical geography, just as I love the view of the Gherkin, the Cheesegrater, the Wad, and the Walkie-Talkie—deceptively kiddie (and, yes, very Cockney) nicknames for buildings that embody an epochal shift in London’s built environment and self-conception. Like some Christopher Nolan movie special effect, these up-thrusting curtain walls of glass, so alien to the city’s skyline for the vast majority of its history, mark the transition from actual to virtual, quite as much as the replacement of the Knowledge by Google Maps.

Anyway, that’s some of London encountered “on the cotton” for you—you now know at least one run, and some of its “points” (of interest). It’s a sobering thought that we haven’t even crossed the river yet, and entered its more celebrated precincts. Don’t stay sober for long: if we project our line in space and time, it tends over Blackfriars Bridge and past the Royal Courts of Justice, on the junction of Fleet Street and the Strand, a neo-Gothic fantasia. After that, it deposits you in the 17th-century pub, the Seven Stars, immediately to the rear. Roxy Beaujolais, the patronne for many years now, serves wholesome fare and cask-conditioned (that’s warm) ale from Adnams brewers, in Suffolk.

This is what you will drink. There’s not much I admire about English mores, but serving beer at room temperature isn’t only estimable, it’s essential. It’s one of those traditions, like licensing cabs to ply for hire and then getting their drivers to systematically alter their neuroanatomy, that remains very distinctive to London, England.

Will Self is a London-based writer