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.