Jack the Ripper is both an ideal and a terrible subject for a major London museum. He’s a potent figure in the city’s mythology and his grisly acts had a pivotal influence on the police, the press and the living conditions of the poor.

But his infamy rests on the murder and sexual mutilation of between six and 12 women, and his anonymity leaves a curator with scant and unseemly material to display: dry police reports and gory photos, madly gloating hoax letters and the flotsam of 120 years’ worth of anti-Semitic, anti-royal or just plain bonkers conspiracy theories.

The Museum in Docklands has made a fair job at setting Jack within his historical context. When Jack began his spree in August 1888, Jekyll and Hyde was on stage, Sherlock Holmes had made his fiction debut and the East End was a mysterious place of grinding poverty and alcoholism, peopled by suspicious foreigners and “unfortunates” (prostitutes) — a scandal to would-be reformers, pruriently intriguing to others.

Newspapers glutted the appalled and fascinated public as the “Whitechapel Murders” mounted, the injuries inflicted ever more extreme. Public pressure found the police wanting and, according to George Bernard Shaw, eventually forced the government to clean up the East End.

This show tempers press and police material with videos of contemporary talking heads discussing prostitution, poverty and the mentality of a murderer. It also puts objects such as mangles and carts alongside butchers’ knives and surgeons’ kits, ostensibly for balance, but actually to make up for the lack of large artefacts directly connected to the Ripper. In the end we’re left with the letters, pictures and theories, and our own prurient interest in the first serial killer.

I confess to a guilty thrill at finally seeing the infamous “Dear Boss” letter in which the name “Jack the Ripper” was first signed in red ink. I doubt that many people will be put off entering the separate gallery devoted to photos of Jack’s assumed victims by a warning about their horrific nature (really only warranted by the pioneering crime-scene photo of the horrifically butchered Mary Jane Kelly).

Does this, though, make us any less morally suspect than the tourists on “Ripper tours” whom this exhibition affects to disdain?

Until 2 November. Daily 10am-6pm. Admission £8, concs available. Information: 0844 980 2151; www.museumindocklands. org.uk.