"This is our archaeological handbook," says Chris Wild, brandishing The Condition of the Working-Class in England in 1844, a muddy, thumbed paperback. "Engels."

This, though, is far from being the only contemporary account of late 19th-century living conditions in this part of inner-city Manchester. In 1870, the Manchester Guardian – as this paper was then known – published a series of articles on the city's slums, opening with a scene of 18 adults and several babies squeezed round a single fireplace. Along with Engels' account, the newspaper's archive reports proved influential in the decision to investigate this site. And, not one to leave an investigation unfinished, the Guardian has today returned to the same streets (Miller, Dantzic and Angel) near the city's Victoria Station.

Soon I'm kneeling on the ground in an area where Engels described "cattle-sheds for human beings". Archaeologists are uncovering some of the worst of these slums, the subdivided cellars where people shared beds or slept in doorways while pigs ate human waste in alleys above. A collection of rubbish – bottles, a woman's shoe, broken crockery – lies on the dirt before me.

Little more than a century ago, this part of Manchester, then the powerhouse of the industrial revolution, was as near to hell on earth as you are likely to get in peacetime. The poor, including thousands who fled the Irish potato famine around 1850, came here for the work. Many of them would have had jobs in a large Arkwright mill on the edge of this site. They suffered industrial injury, cholera, TB and typhus; consumed adulterated food and contaminated water; and lived in a maze of wet, filthy, light-deprived rooms and passages. At the end of Dantzic street was a stone-flagged area that became a playground in the 1880s (LS Lowry painted it as Britain at Play in 1943). The stone flags were to stop illegal excavation and sale of the soil for fertiliser: it contained the mass graves of some 40,000 paupers.

By the 1950s the houses had gone, through a combination of slum clearance and wartime bombing. Today, it's a car park. Meanwhile, in 1863 the newly founded Co-operative Society opened its offices a couple of blocks away. It stayed put, so now a collection of listed buildings, one of them as recent as 1962, fills 20 acres. It is, says the Co-op, the largest regeneration site in Manchester. In 2012 its huge new HQ will rise over the Angel Meadow car park.

Wild, an archaeologist specialising in industrial remains, has taken me and the Co-op's head of planning and property strategy, Ruairidh Jackson, to a heap of soil and rubble from which a bright orange mechanical excavator scoops at the ground. Wild works for Oxford Archaeology, an educational charity that assessed the site for the Co-op to support its planning application.

It is now August, and day three of a nine-week excavation. Even within the profession, industrial archaeology remains a controversial area; some academics, especially, perhaps, historians, still question the need for digging the remains of such recent times.

"They say we've got all the information," says Wild. "But we're testing the texts." The historic maps, for example, are proving inconsistent. Wild hopes they will be able to show the actual house plans, and he is convinced his work will reveal details overlooked by contemporary accounts.

We stop at the foot of a ceramic toilet, dating from the late 19th century and cemented into a small, square floor. Beneath, explains Wild, lies the earth of an earlier pail closet – just a bucket under a plank. Broken drains protrude from the side of the trench, and cellar walls made from poor-quality bricks bow under pressure. These were once homes.

Just one cubic metre of inner-city Manchester would be expected to generate more artefacts than found in a century of excavation at Stonehenge. "There were more people living in this part of Manchester than in the whole of Britain in the bronze age," he says. "This is the archaeology of the masses."

The thimbles and toys, the bits of clothes and china, have a poignant association with known events, and, potentially, named individuals. With such objects Jackson anticipates links with Manchester's People's History Museum, due to re-open soon with a new extension – and with the Co-op's own archive.

"I want the younger generation to see this," says Wild, looking across a row of Victorian lodging-house cellars. "We should help the rest of the world not to make the mistakes we made."