In 1982, the film-maker Roger Graef made the first ever fly-on-the-wall documentary, in 12 parts, about the police. One of the episodes – A Complaint of Rape – showed Thames Valley detectives aggressively questioning a woman with a history of psychiatric treatment who had reported being violated by three strangers. “This is the biggest bollocks I’ve ever heard!” is a fairly representative sample of the police interview technique deployed. The episode caused a public outcry (especially as it was broadcast after a court decision in which a judge accused a hitchhiker of “contributory negligence” in her own rape) and led to the formation of an all-female rape investigation team at the police station in the months afterwards.

It has been seen as a pivotal moment for a revolution in the way victims and their cases were approached and handled. And maybe it was, at least for a while. But it’s hard to say with any conviction that any progress gained has been maintained or built on. Conviction rates for rape are horrifyingly low and there is an ever-growing mass of documentaries and dramas – about historic and recent cases – highlighting the role of the police in creating that phenomenon, be it their negligence, apathy, incompetence, misogyny, active malevolence (in cases such as that of Met officer Wayne Couzens, the killer of Sarah Everard) or any combination of the above.

We can add to this Believe Me, a four-part drama about the women who were drugged and sexually attacked by the so-called “black-cab rapist”, John Worboys. It showcases their preternatural determination to get the justice for themselves and his other victims that the police and judicial system seemed at best wholly uninterested in providing.

Created and written by Jeff Pope, it follows his customarily credible practice of relegating the perpetrator (here played by Daniel Mays, your go-to actor for weak, contemptible male characters, and I hope it is clear that this is praise) as much as possible to the background. “I’m not really interested in trying to get inside the mind of psychopaths,” Pope has said. And why would you be, when the heroism of some ordinary people, and the failings and inadequacies of others – and the institutions the latter build in their image – offer such rich pickings?

Believe Me follows the stories of a few of the 14 women who reported their suspicions that they had been drugged and assaulted by Worboys – indicated by things such as unexplained bruises, ripped tights, lubricant on their thighs, sore genitals and lack of memory after being pressed into a celebratory glass of champagne by their taxi driver, who said he had just won big at the casino. The 14 were themselves a subset of the 100-plus women who eventually came forward when Worboys went to trial and after he was convicted.

Only the first two episodes were available for review. They focus mainly on Sarah (Aimee-Ffion Edwards), who is picked up by Worboys after a night out with her gay best friends, nine months after having her first baby; and young Laila (Aasiya Shah), who gets into the cab alone after her friends thoughtlessly leave her at a club. Sarah wakes up in hospital with no memory of how she got there. When she finds the bruises, the lube, the torn tights, the pain, she reports it to the police – who, it turns out, were the ones who sent her to the hospital after a kindly cab driver dropped her off intoxicated. No, they didn’t take his details. No, they don’t have him on CCTV.

Invasive tests on Sarah follow (director Julia Ford focuses on the clenched face that every woman knows from a smear test, if nothing else), and then a barrage of increasingly sceptical and dismissive questions from officers, especially once she tells them she had a dab of coke at the club. A litany of failures to investigate anything properly follows, of the kind that you wouldn’t dare make up if you were making things up. And then the case is closed. Laila undergoes a similar process, with extra humiliation, as she must repeatedly explain that part of her evidence is that she had her period (and was sick because of that, not heavy drinking) and that she woke up with her jeans button pulled off and her tampon missing.

The women and their suffering – not just initially, but in the months and years to come, a result of the assaults and then of the wider insult of not being believed – are real and vivid. Worboys is given only enough space in the story as is required. A punchy, intelligent script makes it a compelling as well as nonexploitative drama that others would do well to learn from, and which makes Pope’s next project, about the murder of Sarah Everard, one not to fear.

Will it – will either – make a difference to how we treat these rampant crimes? Well, that’s another story.