Few women have had the moment of their deaths returned to more often, and with as much relish, as Mary Ann “Polly” Nichols, Annie Chapman, Elizabeth Stride, Catherine Eddowes and Mary Jane Kelly. In each case their throats were cut, and four of them had their entrails removed. Kelly, the only one of “the canonical five”, as Jack the Ripper’s known victims are called, to die in her bed, was completely mutilated. Forests have been felled in the interests of unmasking the murderer, but until now no one has bothered to discover the identity of his victims. The Five is thus an angry and important work of historical detection, calling time on the misogyny that has fed the Ripper myth.

It is astonishing how little we know about these five, apart from their names. Hallie Rubenhold fleshes out their stories from the scraps that are available: coroner’s inquests (three of which are missing); “a body of edited, embellished, misheard and re-interpreted newspaper reports”; parish registers; court registers; birth, marriage and death records; rate books and the archives of the London workhouses. For accounts of poverty in London she turns to Francis Place, Henry Mayhew and Charles Booth; she gets facts and figures from Mrs Beaton. With the documentary veracity of a set of Hogarth prints, Rubenhold follows the victims’ doomed footsteps from birth to death. Except that there is no attempt to imagine each woman’s last moments, or describe the state of her body, or further the search for their killer. Instead she asks how it is that these women – all of them somebody’s daughter, somebody’s sister, somebody’s lover – ended up alone and destitute on the streets of Whitechapel.

The Police News front page on 17 November 1888.

Their lives are grimly similar: born into hardship, they moved from the briefest of childhoods into a cycle of childbearing, alcohol dependence, poverty, emotional despair and homelessness. They died in hell, but they lived in hell, too – not least, Rubenhold argues, because they were born female: “Their worth was compromised before they had even attempted to prove it.”

Nichols, daughter of a blacksmith, spent her first years in Dawes Court, where Dickens had imagined Fagin living with his pickpockets in Oliver Twist. Her break came when she and her husband, William, qualified for accommodation in one of the newly built Peabody Buildings on Stamford Street in Lambeth. This allowed them, for the first time, an inside lavatory. But after four years of fighting – William was carrying on with the widow next door – Polly left her husband and children and entered the workhouse. There were, Rubenhold shows, few other options available to her. Eight years later, the inquest into Nichols’s death shaped itself as an investigation into her moral character: “Do you consider that she was very cleanly in her habits?” the coroner asked her former roommate. In other words, was Nichols a prostitute and thus deserving of her fate? There is no evidence, Rubenhold argues, that Nichols or Chapman or Eddowes ever worked as prostitutes; the police conviction that the killer targeted women of “bad character” perverted the inquiry. The Ripper’s victims, she suggests, were targeted not because they were soliciting sex but because they were drunk and homeless and – most importantly – asleep. The killer preyed on women whom nobody cared about and who wouldn’t be missed.

Chapman’s story is one of addiction: she might have become middle class had she not become an alcoholic. The daughter of a soldier, Annie grew up in lodgings near the Knightsbridge barracks where six of her siblings died of scarlet fever in three weeks. Her father later cut his throat. She married a gentleman’s coachman, moved to a cottage on his employer’s Berkshire estate, and kept photographs of her children on the mantelpiece. She would stay sober for months and then be found drunk and disorderly in the street: eventually she left the cottage before her family were thrown out. There were, once again, few other options available to her. “What her murderer claimed on that night,” Rubenhold writes, “was simply all that remained of what the drink had left behind.”

They died in hell, but they lived in hell, too – not least because they were female: their worth was compromised before they even tried to prove it

Elisabeth Gustafsdotter, later known as Elizabeth Stride, was a Swedish farmer’s daughter from Torslander. She went into domestic service – the “golden ticket” for a working-class girl – but contracted syphilis. She came to Britain where she found and soon afterwards left (probably due to a scandal) a good position in a house at Hyde Park; she married, and soon afterwards left, a carpenter called John Stride; she set up a coffeehouse that failed. For her final years she supported herself by posing as a disaster victim, which in many ways she was.

Eddowes – who died on the same night as Stride – ran away from Wolverhampton to London where she hooked up with an Irish rover called Thomas Conway. Together, she and Conway, sporting matching tattoos, tramped the country as chapbook sellers: being literate, Catherine was able to write down Conway’s ballads. Five hundred members of her family turned out for her funeral.

No one, after the death of Kelly, claimed to have known her, but it was “easy enough”, Rubenhold shows, for a woman to reinvent herself in the 19th century. Mary Jane probably came from a good family and fell into the wrong hands; whatever happened to her, she left her home in Cardiff (although she claims to have been Irish) and ended up in a west London brothel. To reconstruct her time in the whorehouse – what she wore, what she earned, where she went – Rubenhold turns to My Secret Life, the memoir of the pseudonymous ‘Walter’. A series of setbacks brought her from the West End to the East End where, at 25, she was the youngest and the last of the Ripper’s victims.

The Five is not simply about the women who were murdered in Whitechapel in the autumn of 1888: it is for them. This is a powerful and a shaming book, but most shameful of all is that it took 130 years to write.

• The Five: The Untold Lives of the Women Killed by Jack the Ripper is published by Doubleday (£16.99). To order a copy go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £15, online orders only. Phone orders min p&p of £1.99.