Rarely has a book on Jack the Ripper been written with such visceral anger as this one by Bruce Robinson, the director and screenwriter of Withnail and I: anger at Jack, at “Ripperology”, at the establishment, and anger at the police cover-up that allowed one of the world’s most infamous serial killers to remain free.

From the outset, Freemasons and their secretive organisation are central to Robinson’s narrative: “Masonry permeates every fibre of this conundrum.” In the 19th century, virtually everyone who was anyone was a Mason, including the Metropolitan police commisioner, Sir Charles Warren. Robinson blames “Her Majesty’s executive” for the concealment of Jack the Ripper, all the members of which happened to be Masons: “It was a conspiracy of the system.”

Commissioner Warren was “a lousy cop” and “an aggressive authoritarian who imagined all social ills could be solved with a truncheon”. He was also a keen archaeologist, determined to prove the historical basis for Freemasonry, and had led the search in Jerusalem for King Solomon’s temple, which men who like dressing up in aprons and rolling up their left trouser leg believe was built by Hiram Abiff, the first master of Freemasonry. According to Robinson, Jack the Ripper’s grotesque mutilations of his victims were inspired by a foundational masonic myth associated with the temple: the ritual punishment of three Jewish craftsmen – Jubela, Jubelo and Jubelum – who murdered Hiram and were condemned to death by Solomon. All had their throats cut, one was severed in two, another had his bowels burnt to ashes, and another had his heart ripped out and his “vitals” thrown over his shoulder.

The way Jack the Ripper mutilated his victims was, Robinson says, “the essence of what these murders were”. They were bloody performances, part of what the Ripper termed in a letter his “funny little game”, inspired by the occult mythology of Freemasonry. Which is why senior police officers and coroners – all Masons – were so keen to conceal the precise nature of what Jack did to his victims. Officialdom was covering up for Freemasonry and Robinson sets out to prove that the so-called mystery of Jack the Ripper is in reality “an establishment conspiracy … an agenda to conceal a Freemason,” one of whose murders mocked and perverted masonic rituals and beliefs.

Annie Chapman, who was murdered on 8 September 1888, had her throat cut, her abdomen slashed and her intestines placed over her shoulder. On 30 September, Catherine Eddowes suffered the same fate in Mitre Square, a name redolent of masonry. In addition, her face was mutilated with slashes that “look like a pair of compasses”, masonic symbols that Warren had identified among the stones of Solomon’s temple. Jack then cut off her bloody apron, depositing it nearby beneath a scrawled message, or what Robinson calls a “masonic teaser”. It read: “The Juwes are / The men that / Will not / be blamed / for nothing.” It was a message for Warren, part of “one of the most extraordinary mind-games ever played by two human beings”. According to Robinson, “Juwes” was “an infantile sobriquet for Ju(bela), Ju(belo) and Ju(belum)”. It was an “in-house” wordplay aimed at an erudite masonic historian whose nickname was “Jerusalem Warren”. Appalled, the commissioner ordered that the words be washed off, before they could even be photographed, thus destroying one of the most important clues the Ripper ever left.

Bruce Robinson

Just 48 hours after the murder of Eddowes, the torso of a woman (believed to be Lilly Vass), sawn through at the pelvis, was discovered in the foundations of what would become Warren’s new police headquarters on Victoria Embankment, New Scotland Yard. According to Robinson, the murders of Chapman and Eddowes symbolised the killings of Jubela and Jubelo. The body found in the vaults of New Scotland Yard depicted the killing of Jubelum, who was condemned by Solomon to be “taken without the walls of the Temple and there have your body severed in two”. Known only as the “Whitehall mystery”, it was, writes Robinson, an “archaeologically inspired piss-take”, directed at Warren. The perpetrator was never caught and the police denied it had anything to do with Jack the Ripper. The files relating to the case have since disappeared.

Robinson argues that Warren was less concerned with capturing the Ripper than with ensuring masonic allusions were hushed up, even if that meant destroying vital evidence and endangering the lives of ordinary people. Arresting Jack the Ripper would have “put an entire (and clandestine) ruling elite in the dock – its morals, its monarchy – and would possibly have had the cataclysmic side-effect of extirpating Freemasonry from the judiciary, the police and the royal family for all time.”

No book about Jack the Ripper would be complete without a new prime suspect, and Robinson’s doesn’t disappoint. Step forward Michael Maybrick, a famous songwriter. Working under the name Stephen Adams, he released 50 songs in the 1880s, including such hits as “The Midshipmite” and “They All Love Jack”. Maybrick became masonic grand organist in 1889, a position previously held by Sir Arthur Sullivan.

A bachelor who preferred male company, he was good-looking, talented, intelligent, successful and wealthy: “He was just about the last man in London you’d finger as the Ripper.” But as we know, in a whodunnit it’s always the least suspicious person who commits the crime. He was, like American serial killer Ted Bundy, a “Mr Nice Guy”. But he also had “a catastrophic ego of limitless wickedness”. The Ripper described himself in one of his letters, as a “tall, handsome man”, as was Maybrick. Their handwriting share some of the same affectations, such as spelling the word “Boss” with a long or medial “S”, as in “Bofs”. Robinson’s analysis of Jack’s letters, often viewed as hoaxes, is fascinating and chilling. One of the reasons why the letters have been dismissed as hoaxes is because they were sent to Warren from all around the country. But Maybrick travelled extensively as a singer, touring provincial towns and had ample opportunity to do this.

Historians have always suspected the Ripper had a base in Whitechapel, near his crime scenes. Robinson suggests Maybrick had access to an ideal one. Toynbee Hall, a university for the poor, was conveniently located at the centre of eight murders Robinson attributes to the Ripper in Whitechapel. His suspect would have been welcomed at this institution and free to spend the night there, as were other performers, many of them Maybrick’s close friends. It’s just a few minutes walk from there to each of the murder scenes. Martha Tabram, who may have been Jack’s first victim, was stabbed to death on 7 August 1888 within sight of Toynbee Hall.

According to Robinson, Maybrick concluded his murdering career by poisoning his brother, James, in May 1889 and framing James’s wife, whom he loathed. Michael then informed the authorities that his brother, a wealthy Liverpool cotton merchant, had been Jack the Ripper. Both Michael and James were eminent Freemasons, though the records of both have apparently been expunged: “James Maybrick’s Freemasonry has successfully been kept a secret for 130 years.”

It has to be said that Robinson’s ingenious Ripper theory strains the limits of credibility. He describes in forensic detail a cover-up of breathtaking audacity, a chilling criminal conspiracy to conceal one of the worst crimes this country has ever seen: “Because the British state was rotten to the core, Bro Jack got away with it. Nothing could be allowed to threaten masonry, because the whole venal dinosaur of the Victorian ruling elite couldn’t function without it.”

At the very least one has to admire Robinson’s chutzpah. Most academic historians would break into a cold sweat at the very idea of publishing such an outrageous claim. But his research is undoubtedly impressive and has taken some 15 years. He argues his case with such conviction that it is in the end convincing – although I suspect whether you believe him will come down to whether you subscribe to the cock-up or the conspiracy theory of history. Most historians put the police’s failure to catch the Ripper down to incompetence. If he’s right, it’s the biggest cover-up in British history. If he’s wrong – well, it’s still a bloody good read.

• PD Smith is writing a study of crime and detection for Bloomsbury. To order They All Love Jack for £17.50 (RRP ££25) go to bookshop.theguardian.com or call 0330 333 6846.

Bruce Robinson will be in conversation with Will Self at a Guardian Live event on 14 October.