And now for the third side of the triangle (if the Square Mile can be equated to a triangle, which is pushing it, but you get the idea). From the edge of the Barbican, beneath CromwellTower, the City boundary starts a zigzag crawl along several lesser known streets. The Moorgate area is a compact grid infilled with office blocks, with each passing decade more glassy and more lofty than the last. Much of the architecture is uninspired, but some of the taller towers revel in reflective rectangles and swooping sheen. On Ropemaker Street is "the most Luxurious Health, Fitness and Spa facility in The City of London" (their capitals) for financial types in need of a gentle buffing up. Walk by on a weekday to be surrounded by bustling suits - come at the weekend to encounter cranes and roadworks.
At the Red Lion pub, time once again to make a devious diversion to the north. This is another of the boundary's 1994 extensions, this time to swallow up the entire Broadgate development rather than only some of it. The City side of the road is a fortress of international service industries doing whatever they do behind anonymous ramparts. The opposite bank not so, especially as Islington turns into Hackney where the buildings become increasingly "ordinary", even tumbledown in places. Sun Street genuinely does feel like some kind of border between richer and poorer, ditto Appold Street round the corner. Look carefully and you'll spot evidence of the City's insidious Ring of Steel. There are no blatant cameras, chicanes and checkpoints here, but more subtle one-way systems and blocked off roads. Snowden Street has been pedestrianised rather than allowing vehicles to pass, Vandy Street has been completely grassed over, and the junction with Curtain Road split impermeably to divide Hackney from the City. This is security paranoia as ingrained infrastructure, and may never be reversed.
Look up, that's the Broadgate Tower, the northernmost of the City's skyscrapers as yet with no supporting cluster. Peer over the bridge, those are multiple tracks running deep out of Liverpool Street station. And stare ahead, that's Norton Folgate. No longer a Liberty, this brief peripheral street is under relentless threat of redevelopment. Whilst one bar successfully fought off speculators a few years back, the terrace of cafes and small businesses to the east is slowly being boarded up and will surely soon be reborn as something big and characterless. A brief stroll down Bishopsgate follows, then the City boundary turns left towards Spitalfields Market. Don't worry, we're not stepping inside this tourist-over-friendly makeover. Instead a minoralleyway beckons, just one horse-and-cart wide, increasingly narrow and twisty as it goes. Walking through you can almost imagine you were back in 19th century London, so long as you don't look up above the chimneypots and spot the 21st.
Welcome to Petticoat Lane, or Middlesex Street as the main thoroughfare's better known. If you're expecting a bijou market à la Portobello, think again. This is a much less touristy place, more t-shirts and pan scourers than pashminas and bric-a-brac. Only on Sundays do the traders spillout along the entire street, while on Saturdays a few empty metal-framed stalls are the only sign of impending hubbub. If the shops are shut look out for the individual letters of the alphabet spray-painted onto consecutive shutters. And however much this looks and feels like Tower Hamlets, do try to convince yourself that the council flats and textile wholesalers down the right hand side of the road are part of the richest Square Mile in Britain.
The Aldgate one way system's up next, less gyratory than it used to be, with Braham Street (round the back of RBS) recently replaced by a less-than-inspiring "ribbonpark". There's no need to use the subways any more, not now the traffic island where the City's dragon stands guard has become part of a pedestrian crossing. And then it's onward down Mansell Street - an unexpectedly underwhelming thoroughfare. That's another stack of City flats and sheltered housing on the right, not part of the East End, all run by the Guinness Trust. Expect increasing pressure on London's financial district to spread gradually east into Aldgate, replacing mere housing with sky-rise towers, but for now residential obscurity suffices.
Nearly there. A Travelodge and a multi-storey car park are some of the 'delights' round the back of Tower Gateway DLR, before the proper sightseeing section starts again. The unmistakeable turrets of the Tower of London appear across a major road junction, but the City boundary stays well outside the moat, indeed skirts around the back of the tube station for good measure. Trinity Square Gardens are managed jointly by Tower Hamlets and the City, such is their borderline status. Look carefully beyond the war memorial to find the cobbled area marking the site of the scaffold where Sir Thomas More was topped, just outside the City limits. Across Tower Hill is tourist hell, a flurry of fast food opportunists and souvenir outlets luring in international visitors because they know no better. And so the invisible line passes down to the waterside, where the City boundary meets the Thames, right back where I began. The Square Mile mile may not be square, but its perimeter is six miles of fascinating variety.
Enough of the Thames. The edge of the City bends inland through Middle Temple Gardens, aiming for the very point where Fleet Street becomes the Strand. This spot used to be marked by Temple Bar, the western entrance to the City - originally wooden, then later an ornate stone gateway across the width of the street. When road traffic became important the arched blockage had to go, so it was relocated to Theobalds Park in Hertfordshire and replaced by a tall commemorative plinth. On top is a bronze dragon, very different to all the others to be found around the City's perimeter - more proud, less squat. Most appropriate for the dividing line between political Westminster and big business London, and much easier to drive round.
Chancery Lane's up next. Since 1994 the boundary's run the entire length of the street, whereas before that it wiggled to left and right in an unplanned medieval manner. At the junction with Carey Street outside the Law Society is the precise confluence of Westminster, Camden and the City - a spot also marked by a plaque commemorating the Jubilee Walkway. Various intriguing passageways lead off to either side, well worth a weekday exploration, but for this journey the legal frontages of the main road must suffice. High Holborn creeps up round the last bend, a sudden blast of Starbucks and Specsavers, plus considerably more traffic. The Cittie of Yorke pub isn't as 15th century as it looks, being a 1920s rebuild, although Staple Inn really is Tudor, its gorgeous oak frontage one of the few City structures to have survived the Great Fire.
At Holborn Circus, where a statue of Prince Albert doubles up as a roundabout, we veer left. Not up Hatton Garden, but a full half mile straight along Charterhouse Street. What an eclectic street this is. On the left hand side are former warehouses belonging to the Port of London Authority and "The Central Cold Storage", then several cutting-edge bars and nightclubs. Across on the City side, somehow still standing, the anachronistic sheds of SmithfieldMarket. The General Market building at the Farringdon end has seen better days, and survives solely so that it can be incorporated into some sympathetic future redevelopment. Meanwhile an unmistakeable carnivorous whiff exudes from the Central Market, even at weekends, though don't let that put you off photographing the picturesque cluster of telephone kiosks in the covered arcade.
Crossrail's making its mark along here, with deep interventions in several places which will one day combine to create the ridiculously long Farringdon/Barbican station. Charterhouse Square is rather more peaceful, though definitely pentagonal, watched over by the Art Deco curves of Florin Court. That's the last bit of "comfortable" architecture for a while, because straight ahead are the more brutal towers of the Barbican estate. Its raw-build apartments and windswept highwalks loom large - a modern uprising you'll either love or hate. But rather than heading inside we're turning left, to follow a few hundred yards of the only road in the City of London. Every other thoroughfare within the perimeter is a Lane, a Street, a Yard or something, and quite deliberately not a Road, which makes Goswell Road unintentionally unique.
We've reached the City's northernmost bump, carved out of Islington in 1994 to encompass the whole of the Golden Lane Estate. This is the Barbican's lesser known neighbour, a proper housing estate for more ordinary folk, and constructed approximately one decade earlier. Again concrete is king, with high density maisonette flats leading out to surprisingly green open gardens to create a settlement that would've made Le Corbusier proud. At its heart is Great Arthur House, at 16 storeys briefly the tallest residential building in Britain, still blessed with trademark yellow cladding. It has an acclaimed (but inaccessible) roofgarden, topped off by a curved concrete canopy to cover the water tanks. Enjoy the unexpected suburban panorama as you walk around three sides and back towards the Barbican. And don't think everyone who lives in the City is a banker, far from it.
The City of London's changed in shape several times over the centuries. Its perimeter was once defined by the old Roman Wall, but over the years the boundary has nudged outwards into a less regular shape which sort-of resembles Australia. For purists the Square Mile's area is currently 1.12 square miles, making it the smallest administrative district in England. And the distance around the edge I calculate to be just over six miles, which is ideal for a decent-sized walk.
Let's walk the untweaked edge first, the stretch along the north bank of the Thames. This means starting by the Tower of London, which has never been inside the City and is (obviously) part of Tower Hamlets. The City begins at Tower Millennium Pier, from which it's impossible to walk west along the riverbank because some lumpen redevelopment is in the way. Pedestrians need to retreat to Lower Thames Street, past Tower Place and Sugar Quay, which is best done swiftly. And then a proper treat, so long as the tide's out, because the first access to the Thames offers steps down to the beach. And there really is a beach here, or was between 1934and 1971, for the benefit of poor Londoners who couldn't get to the seaside. I was pleasantly surprised to discover that not all the sand has washed away, although you really wouldn't want to sit amongst the detritus left behind as the water ebbs, so best not bring your bucket and spade. An occasionally flooded walkway whisks you past HM Revenue and Customs, then there's a splendid view back to Tower Bridge from outside old Billingsgate Market. And no, Tower Bridge isn't in the City of London either.
But London Bridge is. Peculiarly the whole of London Bridge forms part of the City of London, right the way from the north bank to the south, so this walk has to nip up an unsavoury back staircase from the waterside to reach the upper span. It's a magnificent diversion via one of the finest views in London, now augmented by the Shard spearing the clouds from close by. A pair of dragons guard the southernmost extent of the City, keeping Southwark at bay a couple of hundred yards further than strictly necessary. There's nothing historic about this spot - the original London Bridge landed a few dozen metres further downstream - but it is a reminder of the medieval structure's mercantile importance.
Retreating to the north bank, modern buildings line the waterside walk in a mostly uninspiring way. The path ducks beneath Cannon Street station for sensory overload. See the snaking line of blue lights embedded in the pavement, listen to the heritage soundscape being pumped from several speakers, and try not to smell the chlorine escaping from the neighbouring gym. On the far side by the Banker pub is your second and final opportunity to walk down onto the Thamesforeshore, unless you've timed it wrong and water's lapping roughly against the steps. The next bit is Walbrook Wharf, the City's waste disposal site, where containers of smelly refuse are loaded onto barges and carted off to Thurrock. If the lights flash and the barrier goes down then the walkway closes and you'd best divert inland.
You'll have to divert soon enough anyway, beyond Southwark Bridge at Queenhithe, which is the sole remaining inlet on this northern curve of river. An underwhelming plaque reminds passers by that King Alfred established his harbour here in the late 9th century, although all you'll see bobbing here now are plastic bottles. The inland pedestrian stretch is grim, however, unless you're a fan of brutalist concrete or of dour dual carriageway diving into tunnels. Moving swiftly on. The riverbank is regained just before the Millennium Bridge swoops overhead. Be sure to investigate the glass obelisk below, its three etched sides dedicated to London's ecclesiastical, scientific and general history. Perhaps investigate the linear steel sundial nearby, but don't be distracted by the funicular railway up towards St Paul's. The Thames path then shrinks to accommodate the Blackfriars one-way system before passing first beneath the railway bridge then its highway counterpart.
Beneath Blackfriars Bridge is the outfall where what's left of the River Fleet enters the Thames, again seen only at low tide, and not without some difficulty. It's also the second point at which a diversion to the opposite bank is required, because Blackfriars Bridge is the only other London bridge that's entirely part of the City of London. To walk the perimeter of the Square Mile properly you need to walk all the way across this 150 year old bridge to the marker on the opposite side. A single dragon this time, perched without ceremony in the centre of the roadway, glaring south. The vista downstream is still blocked by construction work for the new Blackfriars station, whose midriver platforms have yet to be opened up because the solar roof isn't ready. Soon, please.
Back on the north bank we join the Victoria Embankment, the only road to pass directly along the City's Thames-side edge. It boasts twisty iron lampstands and gruff copper lions, and a succession of naval craft recommissioned as floating bars. Ground level evens out beyond Unilever HQ, and that's Inner Temple Garden approaching on the right hand side. Temple is as far west as we're going - that's the legal enclave rather than the tube station (which is resolutely part of Westminster). On weekdays you can cut up Middle Temple Lane, which is a Harry Potter-esque cobbled thoroughfare lined by legal chambers, whereas at weekends that's locked and lesser back passages await. And it's here on the Embankment that the City's 'proper' boundary dragons reside, perched on a pair of Portland stone plinths. These two heraldic beasts were relocated from the Coal Exchange in 1963, and all the other dragons around the perimeter are merely half-size copies. We'll meet more of these tomorrow...