Gwen notices a pregnant woman behaving suspiciously while shopping at H&M, and tackles her to reveal that her "pregnancy" is a bundle of shoplifted clothes under her shirt. PC Andy arrives on the scene to make the arrest, and in passing, tells Gwen about a mysterious death in Penylan: teenager Danny Wilkinson, who was on his way to Roath Park to buy weed, sank into the road just outside a house called Jackson Leaves and suffocated when the asphalt re-solidified around his body. Gwen heads out to investigate, accompanied by Jack, who has just been visiting an old acquaintance named Alexander Martin at the Mercy Hill Care Home. Jack had spotted the elderly, wheelchair-bound Alexander at St Helen's Hospital during the recent zombie attack and recognised him from several past encounters; Alex is not human, but a Kanatian con man who is lying low on Earth in his retirement. He's also a trained medic, and since Torchwood needs a new medical officer to replace the late Owen Harper, Jack hires Alex to work for Torchwood on a freelance basis.
Ianto meets up with Gwen and Jack in Penylan, after checking the Rift sensors at the Hub and confirming that a chronon energy spike occurred in the area at the time of Danny's death. Ianto cuts the body free of the pavement with a molecular cutter and takes it back to the Hub. Ianto has mentally built a "memory house," an imaginary house constructed from metaphorical signifiers that he attaches to people and events; using the house as a mnemonic device, he has memorised the habits of the other people who use the Millennium Stadium's parking bay, and he is thus able to get the large chunk of asphalt into the Hub during a quiet moment without attracting attention. Once in the Hub, he lowers the asphalt into the autopsy room on a winch, and then discovers that there's been another chronon surge in Penylan.
Jackson Leaves was recently bequeathed to married couple Julia and Rob Wallace by Julia's reclusive Aunt Joan, but the house makes Julia feel uneasy for some reason. Rob and his friend Steve had planned to move furniture into the house today, but their efforts are impeded by the police barricades around Danny's body. A nosy neighbour named Gloria Banks tries to gossip with Julia about the teen's mysterious death, but when she snidely points out that she's never seen Julia visiting her aunt, Julia points out that the state of the house indicates that Gloria probably never visited either. Nettled, Gloria returns to her house to wait for her husband Trevor to return home, sits in her living room chair, and spontaneously combusts.
Jack offers to take the bad news to Danny's mother Valerie; on the way, he tries not to think too much about how this area has changed in the decades since he lived here. He slips retcon into Valerie's drink as he breaks the news to her; she will thus believe that her son died in a traffic accident instead of the bizarre truth, and will grieve but move on. Ianto then contacts Jack to tell him about the second chronon surge, and Jack investigates to find Gloria Banks' charred body. Trevor then returns home, and Jack must pull out the retcon again. Julia has seen Jack investigating both deaths, but isn't sure how to respond to the sight of the strange man; while Rob and Steve have been moving furniture, she has been suffering from panic attacks and has hidden in a cupboard, wishing to fade away to nothing.
Jack calls in Alexander to examine Danny's body. In order to create a distraction and slip away from the care home, Alex doses fellow resident Pip Jarret with perception-altering drugs he created from a few common chemicals, convincing him that the TV room's furniture has turned into malevolent giant ants. At the Hub, Alex determines that the pavement melted around Danny's body and then solidified, and that the chronon particle surges that Ianto had detected weren't powerful enough to have incinerated Gloria on their own. Gwen returns home, but throws up when she smells the roast pork that Rhys has cooked for dinner; Rhys understands, and tells her to go back to work and sort through what's going on so it won't be troubling her. Grateful to have Rhys as her partner, Gwen returns to the Hub and researches the history of Penylan. She soon turns up something surprising: almost everyone who's ever lived in Jackson Leaves has died under violent circumstances, except for the elderly Joan Bosher -- and Jack Harkness, who owned the house in 1906.
Ianto returns to Penylan with a portable chronon particle detector, and while he's there, a woman is knocked across the street and killed as if struck by an invisible tram. Ianto is also standing in the ghost tram's path, but he vanishes into thin air before it reaches him. In Jackson Leaves, Rob is losing his temper while trying to assemble a flat-pack wardrobe, and when he hears the bathtub overflowing, he storms off to protest to Julia -- only to realise that the sound is coming from the spare bedroom. Before Rob's eyes, the ghost of a naked woman walks into the room, gets into the bath and slits her wrists. Julia arrives just in time to Rob trying to save the woman's life, but then both the woman and the bath vanish into thin air, leaving Rob soaking wet and grappling with nothing. Stunned, Julia opens the airing cupboard to fetch a towel for Rob, and Ianto falls out, unconscious and covered in a faint sheen of ice.
Rob calls the emergency number in Ianto's wallet, and gets Jack, who is astonished by his story and promises to respond immediately. He and Gwen leave the Hub, taking an assortment of ghost-hunting equipment with them, and forgetting that they've left Alexander stuck in the autopsy room, which is not wheelchair-accessible. On the way to Jackson Leaves, Gwen and Jack see the police dealing with the dead woman on the street, whom they assume is the victim of an ordinary hit-and-run. Gwen compares the incident to her own encounter with ghosts, but Jack explains that the quantum transducer operated on a different principle. Emotional echoes are usually too weak to manifest as anything other than eerie feelings and déjà vu, unless there are other forces involved...
Rob and Julia carry Ianto to the sitting room, trying not to panic even though Julia is beginning to see the ghost of a leering, dangerous-looking fat man. The entire house begins to shudder as if something is hammering to get in, and when Jack and Gwen walk into the house, Rob panics and attacks Jack with a fireplace poker. Jack wrests it away from him, and Rob and Julia, overwhelmed, walk out of the house and leave Jack, Gwen, and Ianto to it. As Gwen tends to Ianto, Jack wanders through the house, recalling the brief period in 1906 when he thought about putting down roots here. At the time, he was having an affair with a woman named Alison, and another affair with a man named Miles; Alison and Miles were engaged, and neither knew of the other's affair with Jack. Jack innocently attended the wedding, wishing them both well, but Alison and Miles both reacted guiltily when they saw him. Terrified that he had given himself away with his reaction and that Alison would destroy his reputation, Miles drowned her in the river later that same day and then turned himself in to the police.
Rob all but drags Julia out of the house, and is horrified when he realises that he's gripping her arm so hard that it's hurting her; he once hit her almost accidentally during an argument, and promised never to do so again. They try to walk away from Jackson Leaves, but Rob had to park his van some distance away due to the police blockade around Danny's body -- and he and Julia discover that no matter how far or how fast they run, they are making no progress along the road. The rain stops falling and instead hangs suspended in the air around them, and a wall of darkness closes in on the house from all directions. Realising that they have no choice, they return to the house and tell Jack what's happening. Jack walks out to see that the world has faded to darkness beyond the Torchwood SUV, and when he sticks his hand into the darkness, it instantly goes numb, indicating that they're all trapped here now.
Jack decides to make the most of the situation and fetch the ghost-hunting equipment and surveillance monitors out of the SUV. Rob retreats to the kitchen, feeling as if he's losing his grip, but Julia helps Jack to set up the equipment as Ianto and Gwen carry it into the house. Jack tries to assure Julia that the woman who killed herself in the bath, Kerry Robinson, died years ago, and that Julia and Rob saw only a harmless image from the past. However, Julia then reveals that the water from the bath got Rob's clothing wet, and before Jack can react, the ghost of the fat man appears behind him, knocks him to the ground and kicks his skull in. The fat man disappears when Julia stabs him with a screwdriver, and Jack then revives.
Jack and Ianto set up the ghost-hunting equipment and then attempt to return to the dining room, only to find that the house's rooms are no longer in an entirely Euclidian arrangement. It takes them several tries before they find the dining room and are reunited with Gwen. Using her laptop, she discovers that the fat man is Rupert Locke, who was convicted of six violent rapes in 1951 and claimed that the house had made him do it. Jack is confused, as he knows that he should have noticed all this violence and death surrounding a house that he'd once owned. Meanwhile, Rob has retreated into the cupboard under the stairs, where he has found a croquet mallet once used by a lodger named Richard Hopkins in a murder spree. Rob is thinking about using it for the same purpose, and then claiming that the house made him do it.
Back at the Hub, Alexander is growing impatient for the others to return, and is also becoming curious about the mysterious deaths. He eventually uses the winch to pull himself out of the autopsy room, and takes the invisible lift up to the plaza, where he pretends to have fallen out of his wheelchair. A young musician named Joe notices him and stops to help, and Alexander sprays a drug he has concocted in Joe's face, making him susceptible to suggestion. Joe drives Alexander to Penylan, giggling all the way, and there, Alexander discovers that Jackson Leaves is no longer in synch with the rest of the world; when he tosses pebbles at the house, they vanish before hitting it. Alexander has Joe wheel him to the house next door, where the teenaged Hannah Ogilvy is home alone. Alexander uses his susceptibility spray on Hannah, who sinks into a state of gloom and watches without interfering as Alexander disassembles the equipment in her kitchen and uses it to build a chronon particle sensor. Outside, the temporal instability is spreading, but using the sensor, Alexander is able to navigate through the safe spots in the ripples and direct Joe and Hannah to wheel him up to Jackson Leaves.
Julia begins to panic when she and Ianto are unable to find Rob. Jack gives her a drink to calm her down, and Ianto and Gwen realise too late that he has dosed Julia with retcon. They make her comfortable in the lounge, and Jack then goes over the situation and concludes that the deaths they've seen are the result of temporal disruption; the woman in the street was hit by a tram that used to run along the street years ago, Danny drowned in the marshland that existed before Cardiff was built, and Gloria was killed in a fire that occurred during the Cardiff Blitz. Ianto then spots a woman in a wedding dress standing in one of the upstairs room, and Jack, fearing that this is Alison, runs upstairs to see for himself. In his absence, Rob emerges from the cupboard and attacks Ianto with the croquet mallet, and when Ianto and Gwen fight him off, Rob locks them in the dining room and goes to the lounge to kill his unconscious wife.
As an experienced time traveller, Jack is able to sense the chronon surges in the house and navigate his way through them. He finds his way to an era in which Jackson Leaves is still under construction, appears underwater and sees Alison drown, and the steps through a door set impossibly into the outside wall to find himself in a 1960s café. There, the entities that are attacking the house take the form of Joan Bosher, claiming that they were impressed by her strength of will and her ability to resist their influence. The entities are from a potential dimension outside reality; they feed on temporal damage, and were attracted to Jackson Leaves by the damage that Jack did by stepping into Miles and Alison's lives. Jack was unaware of the horrors occurring in the house because they hadn't occurred until now; the creatures have only just started feeding, and the damage they are doing has rippled backwards through Time, changing history.
The entities tell Jack to relax and let them feed, but he escapes from the café and returns to Jackson Leaves. Gwen has accidentally stepped through a chronon surge and appeared in the lounge just in time to save Julia, but Jack stops Gwen from harming Rob, aware that he isn't entirely responsible for his own actions. Alexander then arrives with Joe and Hannah, and reveals that his sensor can guide them through the chronon surges and out of the house. Jack sends the others to safety, intending to remain behind and blow up the house with plastic explosives from the SUV in order to prevent the creatures from turning it into a temporal breach. As the others leave, however, the entities influence Rob to believe that the others are dangerous, and he grabs Alexander's sensor and threatens to smash it unless the others hand over Julia and leave. Gwen and Ianto try to reason with him, but the impatient Alexander instructs Hannah to attack Rob, and she tackles him into the temporal disturbance, which ages them both to dust within seconds. The confused Joe then accidentally steps on the sensor, smashing it to pieces. However, Ianto shoots out the light bulb on the house's porch and turns on the SUV's headlights; the patterns of suspended raindrops show the ripples of temporal distortion, including the safe path. Ianto tests his theory by shoving the protesting Alexander's wheelchair through, and then he and the others follow Alexander out to safety.
Jack navigates the temporal disturbances back to the building site where Jackson Leaves is still under construction. The entities take the form of Miles and Alison to taunt and distract him, but he ignores them, telling them that Alison's murder was the result of Miles' weakness and not his own interference. Rupert Locke appears on the site and attacks Jack again, but Jack kneecaps him with a shovel and plants the plastic explosives. The house will still be built, but the explosion will delay its construction long enough to prevent the younger Jack from buying it on a passing whim. This means that he will not have affairs with Miles and Alison in the house, and the entities will not be attracted to the damage caused to their timelines. This in turn means that the entities' presence is now the greatest paradox in the area, and as they turn and try to feed on each other, Jack steps back into the present day and escapes from the house as its timeline reshapes itself.
Alexander shows no remorse for dragging Hannah into the situation and getting her killed, and doesn't particularly care when Jack tells him that he's no longer welcome at Torchwood. Jack considers overdosing Alexander with anaesthetic, but can't bring himself to murder the old man. As he leaves the rest home, he encounters an old man who claims to be Alison's son, and thus learns that she was not murdered in this new timeline. Kerry Robinson did not commit suicide either, and although Rupert Locke is still a rapist and murderer, his crimes were not exacerbated by the entities' influence. A dose of retcon convinces Julia that her husband died in an accident at work, and Gwen and Jack slip her a winning lottery ticket. A student named Nina Rogers arrives at Jackson Leaves looking for lodgings, but Gwen and Jack send her on her way, deciding not to risk exposing anyone else to potential fallout around the house. As Gwen looks sadly at a missing-persons poster with Hannah's picture on it, Danny Wilkinson walks past, still alive, and Jack gives chase when he realises that the teen has nicked his wallet.