In the spring of 1863, toiling away at Das Kapital in the reading room of the British Museum, Karl Marx read again Friedrich Engels's classic indictment of industrial Manchester, The Condition of the Working Class in England. He immediately wrote to his friend to re-congratulate him on a work of steely fury: "What power, what incisiveness and what passion drove you to work in those days. That was a time when you were never worried by academic scholarly reservations! Those were the days when you made the reader feel that your theories would become hard facts if not tomorrow then at any rate on the day after."

Today, the power, incisiveness and passion of Engels's polemic remain undiminished. Far more so than Charles Dickens's Hard Times, Benjamin Disraeli's Sybil, or Thomas Carlyle's Past and Present, Engels's The Condition of the Working Class is the defining text of the British industrial experience.

And, 150 years on, it speaks to our age with painful prescience - not only in its critique of the instability of the free market and the structural inequalities of British society, but in its unrivalled depiction of the inhumanity of capitalism. With Brazil, Russia, India and China experiencing just the kind of breakneck economic growth that transformed British society in the 1800s - villages turning into cities, peasants swapping fields for factories, and mass exploitation grinding out higher GDP - Engels's polemic resonates with terrifying force.

The young Engels had in fact been sent to Manchester in 1842 precisely to rid him of radical sentiments. His father, a conservative textile manufacturer from the Rhineland, had been increasingly concerned about the circle of Young Hegelians Engels had been associating with in Berlin. Instead of dutifully performing his military service, he had succumbed to the beer rooms and lecture halls of Berlin University where the philosophies of Hegel, Ludwig Feuerbach and David Strauss were debated with boozy gusto. All of which led him to abandon his Protestant faith for Feuerbach's religion of humanity, before then falling in with the "communist rabbi" Moses Hess who taught him that modern capitalism was just as dehumanising a force as Christianity. The solution, Hess suggested, was socialism: the abolition of private property and an end to the alienating effects of the money economy. And in the march toward socialism, England - where the industrial revolution had left a deep chasm between rich and poor and where the proletariat was most advanced - would provide the social kindling of revolution. Engels looked to use his two years in the north-west to marshal the material evidence he needed for his emergent communism.

From 1842-44, he worked during the day at the Ermen & Engels mill in Salford, before plunging after hours into the Manchester underworld. "I forsook the company and the dinner-parties, the port-wine and champagne of the middle classes, and devoted my leisure-hours almost exclusively to intercourse with plain working men," he explained. He visited Owenite Halls of Science, spent time with Chartists, watched a brickmakers' riot, and with his Irish lover Mary Burns sought out the human detritus of capitalist society.

He found it on the south side of the city, just off Oxford Road, where some of Manchester's 40,000 Irish immigrants huddled. Burns's confreres were the most exploited, lowly paid and abused of all the city's residents: "The race that lives in these ruinous cottages, behind broken windows, mended with oilskin, sprung doors, and rotten door-posts, or in dark, wet cellars, in measureless filth and stench, in this atmosphere penned in as if with a purpose, this race must really have reached the lowest stage of humanity."

Engels was relentless in charting the "social war" waged by the middle class on the operatives of the industrial city. Workplaces - mills, mines, factories, farms - resembled crime scenes. "Women made unfit for childbearing, children deformed, men enfeebled, limbs crushed, whole generations wrecked, afflicted with disease and infirmity, purely to fill the purses of the bourgeoisie."

He was inflamed by the Manchester middle classes. "I once went into Manchester with a bourgeois, and spoke to him of ... the frightful condition of the working people's quarters, and asserted that I had never seen so ill-built a city. The man listened quietly to the end, and said at the corner where we parted: 'And yet there is a great deal of money made here; good morning, sir.'"

Behind Manchester's "planless, knotted chaos of houses" there was a brutal logic to the urban form: "Cottonopolis" was zoned along class lines to ensure that the rich never caught sight of what they had done to the poor. Manchester's "money aristocracy" lived in the "breezy heights" of Cheetham Hill and Broughton and travelled along Deansgate into town "without ever seeing that they are in the midst of the grimy misery that lurks to the right and the left." Engels understood that the city's spatial dynamics - its streets, houses, factories, and warehouses - were expressions of social and political power. The struggle between bourgeois and proletariat was tangible in street design, transport system and planning process.

Engels wrote Condition of the Working Class back home in Barmen, under the stern glare of his parents; it was first published in Leipzig in 1845. As such it formed part of a broader continental literature detailing the effects of advanced industrial growth on social conditions. Engels aimed the work at the Prussian bourgeoisie in the hope that such a stark depiction would lead them to choose socialism rather than Manchester's free-market fundamentalism.

The book's initial reception was lukewarm with a few grudging reviews in the bourgeois press. It took another 40 years for an English language translation to appear, first of all in the US in 1886 and then, in 1892, in England with Engels hoping the book might save British socialism from what he considered its misdirection by William Morris and the Fabians. Yet in contrast to many of Engels's other works - notably, Socialism: Utopian and Scientific - its immediate influence was limited.

Yet the book now takes on a dimension beyond its obvious historical importance as a work of Victorian reportage and insight into the genesis of Marxism. In one of the largest mass migrations in history, some 120 million Chinese peasants have, since 1980, made their way from the country to the city, and to read accounts of contemporary urban China is to be thrown straight back into the cityscape of Engels. Cancer rates soar along polluted waterways; rivers turn black with industrial effluent; water is unsafe to drink; acid rain strips forests; some 300,000 die prematurely each year from air pollution; a generation of children is being brought up with high levels of lead poisoning. As China assumes the mantel of "workshop of the world", the special economic zones of Guangdong and Shanghai appear eerily reminiscent of 1840s Manchester and Glasgow. Compare and contrast, as the scholar Ching Kwan Lee has done, Engels's account of employment conditions in 1840s Manchester - "In the cotton and flax spinning mills there are many rooms in which the air is filled with fluff and dust ... The usual consequences of inhaling factory dust are the spitting of blood, heavy, noisy breathing, pains in the chest, coughing and sleeplessness ... Accidents occur to operatives who work in rooms crammed full of machinery" - with an account of working life by a Chinese migrant worker in Shenzhen in 2000: "There is no fixed work schedule. A 12-hour workday is minimum. Our legs are always hurting. There is no place to sit on the shop floor. The machines do not stop during our lunch breaks. Three workers in a group will just take turns eating, one at a time ... The shop floor is filled with thick dust. Our bodies become black working day and night indoors. When I get off from work and spit, it's all black."

In discussions of the modern city the voice of Engels resounds equally powerfully. Perhaps his most faithful acolyte today is Mike Davis, whose 2006 book, Planet of Slums, constitutes a searing update of The Condition. Davis recounts with equal vituperation the sanitary state of the modern mass conurbations ("Today's poor megacities - Nairobi, Lagos, Bombay, Dhaka and so on - are stinking mountains of shit that would appal even the most hardened Victorians"), and points to the power relationships underpinning spatial inequality. A chapter entitled "Haussmann in the Tropics", investigating squatter and working-class clearances in contemporary Africa, China and central America, is pure Engels. "Urban segregation is not a frozen status quo, but rather a ceaseless social war in which the state intervenes regularly in the name of 'progress', 'beautification', and even 'social justice for the poor' to redraw spatial boundaries to the advantage of landowners, foreign investors, elite homeowners, and middle-class commuters." In the sprawling, slum and suburb conurbations of India, the main axis of social separation has reverted from race back to class as economic inequality now defines the nature of urban exclusion from Chenai to Mumbai. Behind this process of economic segregation, in Davis's template, are the forces of modern international capitalism - the IMF and World Bank - determined to carve out islands of "cyber-modernity" amid unmet urban needs and underdevelopment.

Similarly, in the developed world, much of Engels's analysis of the urban form reads as a telling critique of the gentrification programmes which entail the demolition of working-class neighbourhoods and curtailing the informal space of the city. Of course, the language has changed: policy-makers talk now of "sink estates" rather than "slums", of "worklessness" rather than "the residuum" and in Britain the forces of progress come in the guise of "New Deal for Communities" or "Housing Market Renewal Funds". Even Engels's adopted city has not been unaffected. While Manchester's revitalised city-centre glistens, Moss Side and Garton have somehow failed to prosper.

The Condition of the Working Class in England is far more than the work of an angry young man confronting the iniquities of industrial capitalism. It is a brilliant polemic by a sensationally gifted 24-year-old applying German philosophy to existing conditions with a sure eye on the revolution to come. As the experiment of 20th-century state communism recedes into memory, like Marx we can at last return to The Condition of the Working Class and appreciate the work on its own terms. To do so is to discover in its economic critique of unfettered markets, condemnation of capitalism's social injustices, angry reportage, and analysis of politics, poverty, feminism and urbanism all the power, passion and incisiveness which Marx rightly heralded.

• Tristram Hunt introduces The Condition of the Working Class in a new Penguin Classics edition.