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On 29 April 1986, three days after Reactor Unit 4 at the Chernobyl nuclear power station went into meltdown and exploded, Vladimir Shevchenko gained access to the site and filmed the ongoing disaster. He shot some of his film from a helicopter, passing directly over the burning reactor. Viewing his footage later, Shevchenko discovered that portions of it were seriously degraded. At first he thought the film stock was faulty; it turned out that the aberrant flashes and blips, and the static on the soundtrack, were the invisible crackles of radiation itself, made visible on the photographic emulsion. Those who were at Chernobyl at the time said that they could feel the radiation, like pins and needles on their skin.

Shevchenko, along with the film and the 35mm Konvas Avtomat camera he used, had all been irradiated. The Ukrainian film-maker died a year later, and his camera is now sealed in a lead-lined casket at a storage facility outside Kiev. Chernobyl's reactor is itself entombed in its own sarcophagus. Shevchenko's film, Chernobyl: A Chronicle of Difficult Weeks, has since been described as the most dangerous roll of film in the world. It is now showing on a monitor at the Whitworth Art Gallery in Manchester, alongside Jane and Louise Wilson's most recent film installation, The Toxic Camera. This focuses on Shevchenko's story, and takes us to the exclusion zone around Chernobyl, as well as to the strange, brutal, abandoned military structures that stand on Orford Ness in Suffolk, where, during the 1950s and 60s, Britain's H-bombs, minus their atomic payloads, were tested to ensure they wouldn't go off or shake themselves to pieces before they reached their intended targets.

The Toxic Camera features interviews with Shevchenko's surviving colleagues, as well as a great deal of atmospheric and sometimes moving incident. The camera glides, rises and falls. It is a witness and guide, leading you on and detaining you. It rises over a structure that once contained a cyclotron at Orford; it skates over dead mud and pebbles. It gets sidetracked, stopping at a snail's shell, at the torn end of a pipe, a boy's face, a curl of rusted razorwire, apples falling to the ground to rot in an orchard in the Chernobyl exclusion zone. A man buries his head in a tangle of bright foliage. He might be crying.

Grim grandeur ... a still from Toxic Camera by Jane and Louise Wilson.

The Wilsons' work is more than just a film. Here is a black, bronze-cast replica of Shevchenko's camera, pointing blindly from its concrete plinth at a measuring stick which, reaching like an antenna towards the ceiling, disappears into the gallery's double-height gloom. More measuring sticks appear in and among the Wilsons' photographs, like divining rods calibrated with chequerboard markings and stripes. They measure nothing, just as the bronze camera sees nothing.

Earlier this summer, I visited Orford Ness with the artists. It is one of the strangest, most haunting places I have ever been. Bunkers and concrete pagodas dot this island of shingle and wetland on the Suffolk coast. Radar was developed here during the second world war, and other secret, experimental work went on in the now decaying buildings. The Wilsons had installed their yardsticks in various places, in sub-basements and buildings without roofs, open to the weather, and amplified the ambient sounds of wind and metal that echo through the buildings.

Orford feels like the end of the world, a place of grim grandeur and melancholy. The cranes of Felixstowe docks rise to the south. Sizewell nuclear power station dominates the horizon to the north. One place leads to another, Orford to Chernobyl. Journeys to forgotten spaces and liminal zones have been the subject of the Wilsons' work since the beginnings of their joint career, in the early 1990s. The sisters have taken us from Kings Cross bedsits to the abandoned Stasi headquarters in Berlin, from a Russian cosmonaut training centre to a graffitied modernist folly in Peterlee new town. At the Whitworth, they also show us the abandoned Soviet city of Pripyat, near Chernobyl. Here is a ruined classroom and an abandoned, rotting library. Here is civilisation in ruins.

In a second, 2011 film installation, with text by Eyal Weizman (and Shumon Basar), Face Scripting: What Did the Building See, the Wilsons' camera tours the sleek anonymity of a modern hotel in Dubai, where a Hamas operative was assassinated by Mossad agents. The camera sweeps the carpet, captures the light on louvred blinds, searches for room 230 where the deed was done. It is just another hotel room. It could be anywhere. Opposite the screen, a dangling TV monitor replays real CCTV footage of the incident. This, too, seems anonymous and generic, with its surveillance footage of corridors, parking zones and lobbies, and captured images of the blurry hit squad, looking like tourists or business guests, come to do their wet work.

These two film installations are displayed in large, partially enclosed rooms-within-rooms with translucent walls, with mirrors at right angles to the screens. They feel as much like diagrams as real spaces. The light leaks in and the images thrown on the screen are reflected and multiplied by the mirrors. Get up close and you see yourself there, too, your repeated image bending away into infinity. The effect is like watching the bright windows of a train passing in the night. This sense of duplication and reflection is integral to the artists' work. It feels like metaphor – and it feels like a trap.

The Wilsons' film installations haven't always been so effectively staged. Here, they have made great use of the difficult architecture of the Whitworth's complicated spaces.The exhibition design, as much as the things in it, feels like a kind of fiction. We could be in a story by JG Ballard or a novel by Don DeLillo, a movie by Tarkovsky or by Kubrick, a conspiracy thriller or a drama-documentary. What the Wilsons document, they also twist. There is no objective view. Nowadays, instead of featuring on-screen themselves, we are made aware of their overriding subjectivity, an implacable and sometimes merciless view. It is hard not to feel the sadness of the world here, the misery of the modern age, in these rooms of photographs and measuring rods, the dead bronze camera and the filmed trails of murder, nuclear disaster, cold wars and hidden wars. You get lost in it all: there is no end to its bleak and unremitting architecture.

• This article was amended on 24 October 2012 to credit Eyal Weizman and Shumon Basar, along with Jane and Louise Wilson, for the film installation Face Scripting: What Did the Building See.