“May you never die until I kill you.” These are the eight chilling words, scrawled on a piece of paper by serial killer John Sweeney, that give ITV’s new true crime drama its name. Until I Kill You is the story of Delia Balmer, the sole known survivor of Sweeney, who is now serving life for his crimes. Actually, as is very clear from the harrowing events we witness, Balmer is also a victim of the British criminal justice system, which spent years gaslighting and further traumatising her in various courts and police interview rooms.

She has, in short, suffered for most of her life. Delia’s experiences may have been extreme – to the extent that she almost died on a number of occasions, and has been left with pain and disfigurement from the injuries Sweeney inflicted on her – but we all know only too well, from any number of other real-world cases, that the failures of the system to defend and protect women only vary in degree. In at least two other cases (those of Melissa Halstead and Paula Fields, which are alluded to in the drama), Sweeney did murder them, dismember their bodies and dump their remains in canals in Holland and London.

This is a harrowing drama. It’s also a compelling one, because of the constant jeopardy that Delia finds herself in. Played opposite Shaun Evans’s Sweeney with a kind of wary sympathy by Anna Maxwell Martin, Delia is not an especially likeable person. Indeed, she’s often rude and oddly obsessional about her few belongings; hers is a life lived with an extreme minimalism. Maxwell Martin treats her as, one imagines, Delia would wish to be – as a unique person, and an unusual one, refreshingly nuanced, in that sense, and Martin vividly captures the shades in her personality – far from the kind of one-dimensional “Female Victim #1” that appears in too many such documentaries and dramatisations.

Delia is irritable, reacting with startling scorn to well-meaning strangers when they ask if her accent is American, and she then lectures them on her family history – more Australian and Canadian than American, as if they should have discerned that from an initial greeting. She is awkward with most of her workmates, and declares at one point that she’s never loved anyone because she doesn’t believe in “that mushy stuff”. A kind of ageing hippy, then, in the early 1990s, aged about 40, who loves to travel and to dance and who meets a charming Scouse carpenter in a London pub. She meets Sweeney’s family, and he moves in, in every sense. We watch with a mounting sense of doom as he slowly develops his coercive control over her, like a cancer, culminating in tying her to the bed and periodically raping her.

Her friends try to help, but the police don’t take it that seriously at first, and even when they do, a judge lets Sweeney out on bail. He absconds, and for years Delia lives in fear of him, until one day he turns up and attacks her with an axe and a knife, leaving her with life-changing injuries. In her various testimonies in court, we learn exactly what kind of a manipulative monster Sweeney is, with the added horror of his habitual sketching of the women who fell under his control, including of their dismemberment.

It is these explicit, annotated drawings that help convict him in the end, and the cold words on one of them give rise to the title of this superbly constructed piece. In that sense, Sweeney is a kind of stereotype serial killer – Dennis Nilsen (David Tennant in the superb Des) did the same – but obviously still unfathomable. At moments, Evans renders Sweeney as simply insane, a torturer himself tortured by not understanding why he does what he does; but as we also see, Sweeney is always purposeful and determined in his murderous work, and his moments of repentance and tenderness just fake. The discovery by the police of a sort of “murder kit” secreted in Delia’s flat – ropes, bleach, gloves and a hacksaw – proves his intent beyond doubt.

In Until I Kill You, even Sweeney’s eventual final trial at the Old Bailey for his other crimes is filmed with a dark, claustrophobic feel that matches the sense that Delia is still emotionally imprisoned by Sweeney, decades after she first encountered him. And, in the brilliant performance by Maxwell Martin, Delia remains defiant but unhealed by a kind of survivor’s anger, rather than guilt. When she cries out, “Everyone cares about the dead ones – maybe I should have died and the police would give a f*** about it,” it’s hard not to feel like she might be right.