The ley lines, the hallowed dome of St Paul’s, packs of hungry dogs – and a tipsy surveyor in the 1930s ... these are the invisible forces shaping the City’s skyline

The last piece in the jigsaw” is how architect Eric Parry described his design for 1 Undershaft, the tallest building in the City of London, when it was unveiled this week. It will crown the planned “cluster” of towers, standing right between the Cheesegrater and the Gherkin. But it’s far from the final piece – in fact, it’s only the beginning of another building boom.

North of the Gherkin, a tower nicknamed the Can of Ham for its odd tubby form is currently being built. Designed seven years ago by Foggo Associates, the 24-storey spam tin has been revived by one of the world’s biggest pension funds, TIAA-CREF. Meanwhile, cranes are conjuring the 38-storey Scalpel – a stunted cousin of the Shard by US architects Kohn Pederson Fox. “The Skyline Refined” trumpets its construction hoarding, showing the glass blade reaching to the skies, as if poised to slice up its neighbours.

Which might not be a bad thing, given what’s coming next door. The gargantuan staggered slabs of Make’s 40 Leadenhall Street, for Henderson Global Investors, will form a building more than twice the Scalpel’s bulk. Dubbed Gotham City, for the sense of dystopian gloom it will cast over all who see it, it has the unfortunate quality of being a groundscraper and a skyscraper at the same time – and resembling a corpulent grey heap.

Some of the biggest pieces are still missing from the chessboard, as the planning office struggles to keep up with what developers are throwing at it. 22 Bishopsgate was recently granted permission on the site of the ill-fated Pinnacle, where a seven-storey concrete stump has stood since construction stalled in 2008 – a mocking relic of the last banking bubble. It will combine the total internal area of the Cheesegrater and the Walkie-Talkie inside one slab that’s 80m-wide and 278m high – enough space for 12,000 people.

22 Bishopsgate was fiercely opposed by the neighbouring boroughs of Islington and Tower Hamlets, along with Royal Parks and Historic Royal Palaces, who feared its “broad-shouldered” profile would create a “solid backdrop” to the Tower of London, compared to the previous scheme’s tapered peak. Even Heathrow, 15 miles away, complained that its heft would interfere with radar coverage. Permission was granted nonetheless.

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Besides blocking the sky, there will be consequences on the ground. After the Walkie-Talkie was found to create gusts of wind that can sweep people off their feet, it raises questions about the effect this new wall of giants standing shoulder-to-shoulder will have on just being able to walk down the street.

Eric Parry has identified an area for an “artist’s wind-baffle commission” at the most hazardous spot on the 1 Undershaft plaza, while Richards assures that wind issues are being taken more seriously. He, however, is a fan of the buildings being so close. “There’s a real psychology of proximity in the cluster,” says Richards. “The insurance industry, more than anything else, relies on face-to-face contact. There’s a culture of huddling together for collective benefit.” Soon, brokers won’t even have to leave the office – they’ll be able to conduct meetings through the windows.

With all these projects coming at once (bringing over half a million sq m of floorspace) Richards realises clearer guiding principles must finally be set out. For the first time, he has begun to model what all the City’s constraints actually look like in 3D, developing a kind of “jelly mould” for all future developments. He began by drawing a mountain-shaped dome over the cluster, then went around the distant viewing points one by one, “chipping away at the foothills”.