Some weeks ago, the director of the Tate galleries, Sir Nicholas Serota, had a spat with people living near Tate Modern that could have come from a satirical novel. They had complained that the gallery’s new 10th-floor public balcony looked directly into their glass-walled flats, which are in a nearby, slightly older tower complex and are each worth up to £19m. Serota tartly replied that the residents should “put up a blind or a net curtain”, “as is common” in most homes.

Amid all the row’s diverting details – such as the advertising of the block of flats as “adjacent to … Tate Modern” – the fact that the elite of London’s arts and property worlds should be jostling for precedence in the sky above the capital was rather taken for granted. Yet until this century, London was not a city where many rich people lived in high-rises, nor one where seemingly every major new public building came with a viewing platform. Like other flat, sprawling cities, London was low‑rise, its hazy vistas largely uncommodified, and enjoyed mainly by council tenants in derided tower blocks.

In this panoramic, at times jaw-dropping book, Stephen Graham describes how in recent years the built environment around the world, both above and below ground, has become dramatically more vertical – and more unequal. From miles-deep gold mines in South Africa to oligarchs’ basements in Belgravia, from American schemes for lethal military satellites to Bangkok’s elevated railway for the wealthy, the Skytrain, Graham lays out a landscape where architecture reflects and reinforces divisions with ever greater brazenness.

Many of his examples are as dystopian as anything in the bleak prophecies of JG Ballard. A resident of a “luxury fortified apartment complex” in Rio de Janeiro watches tracer bullets, fired by feuding drug dealers in a favela far below. “They are beautiful!” she says. “We have a free firework display almost every day!”

Graham is a professor at Newcastle University and writes in an academic but compelling style. Familiar from fellow leftwing Verso authors such as Mike Davis, his approach combines disgust, cool analysis and something close to exhilaration at the spectacularly awful state of the world. Occasionally, Graham ties himself up in pious and over-exact jargon. Shanty towns, which increasingly occupy the vertical city spaces the rich don’t want, such as unstable mountainsides, are defined as “collective claims to space … necessarily mobilised by the poor and marginalised”. But more often his phrase-making is sharp and memorable. He sums up the increasing segregation of cities by height as “class war from above”.

HIgh-end … Manhattan skyline, as seen from a bathroom at 432 Park Avenue. Photograph: PRCo

As many cities in both rich and poor countries have become ever more congested and polluted, he writes, the wealthy have “seceded” upwards: into “islands” and “archipelagos” of residential towers, hotels, private clubs, roof gardens, restaurants, swimming pools, even heliports. These overbearing new structures offer the prosperous light, views, fresher air, safety from crime, and speedy travel – while often, by their very existence, reducing the availability of these to everyone else. Anyone who has trudged along a draughty, overshadowed street at the base of a block of luxury flats will know what Graham is getting at.

Until the 21st century, it was widely assumed that private towers were for offices. But the diminishing physical needs of many businesses in the digital era, and the realisation that residential and leisure towers needed fewer lifts than packed office blocks, leaving more space to let, contributed to a shift by landlords and developers. Graham also explains with lucidity and gusto how improvements in lift technology are making taller and more exclusive buildings possible. The second-tallest in Manhattan is 432 Park Avenue, an almost impossibly slender stack of apartments, each one taking up a whole floor. Even-handedly, Graham includes a photo of the astonishing skyline view from one of the bathrooms; and a picture of the whole building, which looks like the 1 % giving the rest of us the finger. Another, older, even less tactful elite eyrie in Manhattan, sadly not discussed in the book, is Trump Tower.

Before lifts, the upper floors of buildings were for the poor. When tower blocks first became common, in the mid-20th century, they were a housing type tested mainly on the working class, with mixed results that were quickly presented by opponents of modern architecture and state housing as uniformly disastrous. Like other leftish architecture writers such as Owen Hatherley and Douglas Murphy, Graham explains well how this trashing of the tower block took place. But he never quite clarifies whether it was a deliberate strategy to, as he puts it, “clear the way for the elite takeover of the urban skies”; or whether the boom in luxury towers – which began several decades after the great panic about proletarian high-rises – has just been developers belatedly spotting a vacuum and taking advantage.

Below ground, Graham also sees the rich expanding into a realm previously associated with the poor. In London, basement living is coming to mean privileged seclusion rather than Dickensian squalor – although the scale of the change is often exaggerated by breathless press coverage, for and against. According to Graham, in 2014 there were 450 planning applications “for major residential basements in Kensington and Chelsea”, the borough with the greatest appetite for “iceberg houses”. In 2012, a single Toronto suburb had “30,000 illegal … and often dangerous basement apartments occupied by new Canadian migrants”. In many countries, the homes of the rich have come to dominate the media space as well as the city itself.

Graham’s focus on the malign sides of ever more vertical urban life is powerful and thought-provoking

For several chapters, this dizzyingly restless book moves beyond architecture and explores the impact on cities of satellites, drones and helicopters. One of Graham’s main themes is the growing influence of military technology on civilian life. The descendants of “military GPS systems, used to drop lethal ordnance on any point on Earth”, he points out, are now embedded in phones and cars. Police helicopters are deployed in troubled American cities, such as New Orleans, with a mindset and equipment derived from the wars in Iraq.

Graham’s focus on the malign sides of ever more vertical urban life is so powerful and thought-provoking that only occasionally do you realise that he has left lighter topics unexamined, such as the possibility of consumer treats arriving by drone, or the opening up of cities to public scrutiny from above by childishly thrilling devices such as the new levitating observation deck in Brighton. The book also lacks on-the-spot reportage, taking most of its material instead from written sources. Perhaps that’s to be expected of a work that covers a vast geographical area, and which, for all its thematic daring, is still in some ways an academic book: incremental, careful to back everything up, reluctant to be too colourful or impressionistic.

A man lifts weights on the balcony of the 28th floor of the abandoned ‘Tower of David’ skyscraper in Caracas, Venezuela. Photograph: Jorge Silva/Reuters

Here and there, like a shanty builder discovering a new urban crevice, Graham finds a little space to discuss how the polarisations of the vertical city can be resisted. In Caracas, Venezuela in 2007, a 45-storey building intended to contain lavish flats and a helipad, but left unfinished and abandoned after the death of its developer, was squatted instead by hundreds of families. The gaping tower became a vibrant improvised neighbourhood, complete with small businesses and churches, which survived until its inhabitants’ eviction in 2014.

Less reassuringly, Graham recounts how Mohamed Atta, a leader of the World Trade Center attack, was for years before 9/11 a ferocious critic of high-rises. A holder of degrees in both architecture and urban planning, he regarded such buildings as destructive of cities’ ancient virtues – as do many conservationists and urban activists, and as, in some ways, does Graham himself.

With climate change, he argues gloomily, the appeal of air-conditioned citadels in the sky will only grow. “Apartheid atmospheres” – another striking coinage – are here already, he suggests, as the privileged of smoggy China and the sweltering Middle East increasingly retreat into sealed enclaves with processed air.

The book ends down a mine, where much of the wealth that is building the world’s most vertical and hubristic cities originates. In South Africa alone, Graham writes with a flash of old-fashioned leftwing outrage, on average five miners die each week. It’s a sobering moment in an often dazzling book. Cities feel different once you’ve read it.

• Andy Beckett’s Promised You a Miracle: Why 1980-82 Made Modern Britain is published by Penguin. Vertical is published by Verso. To order a copy for £16.40 (RRP £20) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.