Given our seamy obsession with serial killers, real and fictional, one would expect the crimes of Stephen Port to have made more of a mark on the national psyche. Port was convicted in November of the rape and murder of four young men in Barking, east London over a 15-month period. His modus operandi was cold and calculating: He would contact men on gay hook-up sites and incapacitate them with 'date rape drug’ GHB, before sexually assaulting and murdering them. A further seven men were drugged and/or raped but lived. Port is serving a whole-life sentence; he will die in prison.

What makes these crimes particularly shocking is that the Metropolitan Police apparently had multiple chances to stop them and failed each and every time. Officers allegedly routinely ignored or dismissed information that could have led to Port’s apprehension. Unforgivably, they not only had Port in custody at one point, he was jailed for perverting the course of justice. And still he was able to carry out his murderous campaign under the noses of the authorities.

These revelations are what made Thursday night’s BBC documentary, How Police Missed the Grindr Killer, at turns compelling, depressing and infuriating. 'Stephen Port took Jack's life but they let that happen,' one victim’s sister attests early on. 'As far as we're concerned, they're just as guilty as him.' If that sounds unduly harsh, Steven Grandison's film documents a police investigation that appears to have been so breathtakingly incompetent it's hard not to conclude that officers share some culpability.

Their catalogue of failures is lengthy and grim. In June 2014, Stephen Port called 999 to say he had found the body of a young man outside his flat. The victim was Anthony Walgate, 23, and Port had found him there because he had left him there. Port was questioned; bruises and blood were found on Anthony's body -- but the death was deemed a drug overdose. Detectives later discovered that Port had arranged to meet Anthony on a dating site on the night in question and they brought him back in for questioning. Astonishingly, they believed his new alibi: Anthony had taken GHB at Port's flat and died, and Port had dragged the body outside lest he be suspected of murder. He was convicted and briefly jailed for obstruction of justice.

When Sarah Walgate pointed out her son's phone was missing, police told her it was 'too expensive' to trace it. The same reply was given when she urged forensic examination of her son's and Port's laptops. A grieving mother had better investigative instincts than the detectives tasked with probing her son's death.

Port went on to kill Gabriel Kovari and Daniel Whitworth in the same manner. In each case, he dumped the body in a graveyard a few hundred metres from his flat, positioning the men against the same wall in the same stance (they were even discovered by the same elderly dog-walker). Port invented two implausible narratives: First, that Gabriel had gone to Spain, then back home to Slovakia, whereupon he died of a 'mysterious disease'. Then, he planted a fake suicide note on Daniel's body, detailing how the pair had been lovers, Daniel had watched Gabriel overdose, and was taking his own life out of shame.

Barking and Dagenham police bought Port's latest concoction, and ignored Daniel's family when they said they couldn't be sure the handwriting on the suicide note belonged to him. A detective later told a coroner's inquest that he hadn't ordered DNA testing on the bed sheet Daniel's body was discovered on. Even after the coroner handed down an open verdict, the Met refused to reopen the case.

While officers continued to display Barney Fife-esque credulity, Gabriel's friend John Pape did their job for them, establishing links between the deaths of Anthony, Gabriel and Daniel. When he presented the evidence of a serial killer on the loose, police sent him away. Pape turned to Pink News and LGBT group Galop, asking them to use their relationship with the force to raise the alarm. The newspaper and campaigners were similarly disregarded. No public warnings were issued to the LGBT community in Barking.

The family of Jack Taylor, Port's final victim, scarcely received better treatment. The 25-year-old was found next to the same cemetery as the others, sitting against the wall, and Port had planted a syringe on him to throw the police off his tracks. Not that he needed to. Jack's sister says she contacted the station the following week to find 'nothing had been done for 11 days, no investigation. It was just a case of: Jack had gone and sat there, done an overdose, and that was that'. This was despite Jack's family insisting he did not use illegal substances and in fact was 'anti-drugs'.

Predictably, the family undertook their own enquiries and uncovered the same evidence as Pape. They too were given short shrift. The Taylors, by their account, had to badger the police to take interest in CCTV of Jack's final hours in which he was seen walking with another man. Officers insisted the two men had parted ways and Jack had gone alone in the direction of the cemetery. What the video actually showed was that Jack remained with the man and when the CCTV was made public, the man was identified and arrested within two days. The man was Stephen Port.

Sarah Walgate sums up the unanswerable charge sheet of stupidity and apathy: 'Stephen Port is a liar and yet the police continually believed him... If Anthony had been a girl, left outside like trash, they would've put a lot more effort into it. But as they were all young gay boys, they didn't. They did nothing.'

Like most gay men today, I thought the police had moved on from the bad old days. They had been retrained; old attitudes and those who held them had died out; lesbian and gay police groups flourished. If anything, I wondered if all this outreach was the best use of overstretched police resources.

What fools we have been. We got our gay marriages and gay Tories and thought that was it. We'd won. Pride was now just a fun day out, with maybe the occasional heckle over the blood ban. The Stephen Port murders, and the indifference of Barking and Dagenham police, suggest we may have been fooling ourselves.

Four gay men were murdered in strikingly similar circumstances and their bodies dumped (in one case literally) on the killer's doorstep. The police response was so inept that it forces you to wonder whether there were was something more than just incompetence – was there an element of homophobia or some weird indifference or even callousness towards gay victims?

The Met did not participate in the documentary but has reported itself to the Independent Police Complaints Commission and 17 of its officers are now under investigation. However, the force told the BBC: 'We have not waited... to enhance understanding of... drug-facilitated sexual assault.' Officers, they added, were now 'trained... about this type of crime with the help of... LGBT organisations'.

Perhaps the most galling aspect of these killings was their location. They did not take place in rural Alabama or the Colorado mountains; there will be no Oscar-baiting dramatisation starring Sean Penn as a small town sheriff wrestling with his prejudices as he pursues a killer. This happened in London. The city that's meant to be all Soho bars and rainbow flags, a never-ending coming out party with its own transport network.

After so much progress, it feels like nothing has changed. We're back to Michael Boothe and Christopher Schliach, and the murder spree of Colin Ireland, the early 90s serial killer who targeted gay men because, he told officers, they 'keep their mouths shut and don’t tell the police things'. It was hard to watch Thursday night's programme and not conclude that there's still one way to get away with murder in this country, or get away with it for longer: Kill a gay.

Stephen Daisley will be writing regularly for Coffee House. He is also a columnist with the Scottish Daily Mail.