The Doctor and Amy discuss London - in 1963, the coolest place on Earth - even the galaxy! Amy wants to see John Lennon. The Doctor asks why nobody ever wants to see Ringo Starr. The TARDIS materializes in London in 1963, but something is wrong.
London is inruins. The sky is orange and cloudy. Smoke billows everywhere. A nearby shred of newspaper declares it to be the "End of the World". Daleks have destroyed Earth. The Doctor declares that this is impossible. They don't have this kind of technology.
Suddenly, a young woman appears, chased by new red Daleks, resembling the drone Daleks revealed in Victory of the Daleks. The red Dalek announces that the last human alive must be destroyed. She lures the Dalek near a pile of dynamite and runs to a trigger, which she depresses, detonating the dynamite. The Dalek is surrounded by explosions and is immobilized. It screams and seems to die. She jumps down a manhole as more Daleks appear.
Amy encourages the Doctor to follow her and see what's happened. They are unable to reach the manhole because of the sudden appearance of a host of Dalek drones.
Amy and the Doctor sneak around to a precariously balanced, black taxi cab. They push what's left of it into a barred tube station entrance, smashing the wooden planks and leaving room for Amy and the Doctor to go to the underground station.
They catch up with Sylvia, which is the last person alive, and she explains that the world military was targeted and destroyed instantly while pockets of average people managed to survive a while longer. When the Daleks invaded, they came through a shredded sky and blanketed the sky until it was dark with Daleks. Earth was destroyed. She wants to know how the Doctor and Amy survived but the Doctor says they were just spending time 'away'. The Doctor wants to know how Sylvia survived. She says people make do when they are forced to. Daleks appear and Sylvia runs down an empty corridor undetected by the Daleks. The Doctor and Amy are not as quick and must follow without being detected by the Daleks.
When they catch up to Sylvia, she says the electrified train track must be discharged to prevent their electrocution if they are to escape down this corridor. The Doctor rewires a terminal nearby by hand and the three run down the track to a trap Sylvia has set for the Daleks involving dynamite. The Doctor forces Amy to climb up the manhole Sylvia first entered from the surface, just as Daleks appear. Sylvia orders them to run as she is exterminated by a Dalek death ray. The Doctor is distressed to see her die and calls out, but is left with no choice but to climb after Amy as the Dalek triggers the trap and the tunnel explodes.
Amy and the Doctor sneak their way back to the TARDIS, avoiding patrolling red Daleks and the Doctor hastily looks up the source of their invasion power - he traces it back to Skaro, the Dalek home planet. Amy feels sick and coughs but the Doctor comforts her as if he doesn't know what's really going on - she is fading from existence. The Doctor grimly states that they must go to Skaro and prevent Earth from being destroyed by stopping whatever power source the Daleks discovered to mess with locked time periods.
They appear on Skaro and Amy feels worse when they exit the TARDIS. The Doctor explains that when they walked on the destroyed 1963 Earth time, Amy became a paradox - she shouldn't exist now - but the TARDIS can protect her as a time traveler for a short period of time. If the Doctor can collect Dalek parts, he can assemble a crude device that should stave off her non-existence a while longer. The Doctor runs through the active Dalek factory, collecting spare parts and returns to Amy. He constructs a sort of Chronon bracelet out of the parts and equips her with it. Amy still fades to invisibility off and on, but she is apparently more stable with this device.
The Doctor and Amy explore the building a bit more and discover the Dalek 'librarian' - source of all data for the Daleks in this city. It resembles a giant, emotionless, goat-like eyeball scanning a series of observation computers. By sneaking around its sight and reprogramming the security codes the Doctor is able to confuse the eye and use it as a digital window to view the top floor, where the Dalek Emperor appears. Amy comments that this Dalek appears large and the Doctor replies that it's an occupational hazard - part of sitting on a throne all day. As they leave to go to the top floor, Daleks seize them in the lift and declare that the Dalek Emperor will see them. The Doctor replies 'just the dictator I wanted to see.'
The Dalek Emperor seems to brag about knowing the Doctor. The Doctor says, well that saves time. He doesn't have to explain who he is again. The Doctor converses with the Dalek Emperor and acts afraid of the Daleks' power source, trying to make the Dalek Emperor to reveal it. The Dalek Emperor proudly obliges and reveals the Eye of Time. The Doctor is shocked - this was what the Time Lords once had. It is more powerful than the TARDIS, more powerful than any other source of power, some speculate the heart of all time and space. How did the Daleks acquire it? The Dalek Emperor declares that the Time Lords lost it and now the Daleks are the new Time Lords.
Amy and the Doctor leap into the Eye to escape the Daleks. They appear back in time in the same city - Kaalann, the capital city of the Daleks, just before the Eye was brought to Skaaro. The Doctor declares that if they can delay the Daleks from placing the Eye in their control center at this time, they can buy a window to stop the Daleks from acquiring it as a power source.
In the ruins of Kaalaan's floor surrounding the control center, a noxious looking liquid appears in fissures in the ground. The Doctor and Amy devise a crude battery from Dalek materials to draw power from the fissures and charge the control center prematurely. As the Daleks enter through time with the Eye, they are vaporized by the Doctor's trap and the Doctor seems to indicate this is a good thing for the time being. They find the Dalek 'librarian' again, this time guarded by strange gooey plants which whip their heads and attack nearby entities.
Avoiding these and smashing the all-seeing Dalek eye window, a sort of Dalek pupil bounces out and the Doctor says he can reverse-engineer it to blind all the Daleks. The Doctor orders Amy to collect a Dalek eye stalk and Dalek blaster arm which he can use as components of a universal Dalek-blinding device. Amy explores the ruins of the Dalek factory, avoiding the plants and high-alert red Daleks to acquire pieces from the strewn Dalek armor, then returns to the Doctor. Amy's partial invisibility seems to save her from danger at times, but she continually fades toward non-existence. The Doctor works quickly to build the device, then orders Amy to insert the device in the ruins of the Dalek Emperor to activate it. The Doctor and Amy sneak their way to the top floor again, where Daleks anticipate the Eye of Time to be lowered into the control center.
Amy just avoids Dalek guards and does as she is told. When the librarian eye is attached to the Dalek Emperor's casing, it shoots beams into the sky and all the red Dalek guards are temporarily immobilized from shock. They begin screaming 'The Daleks are under attack' and that their vision is impaired. The Eye of Time hovers in place, up by Amy and the Dalek Emperor's throne. The Daleks shoot wildly then stand still firing in place, helplessly blind. The Doctor runs around the beams as the Daleks shout at him and makes his way to the control center, where he is able to use the sonic screwdriver to damage it. Surges explode from the control center of the Eye and Amy begins fading into non-existence. He races up to the now hovering Eye of Time, near the Dalek Emperor's throne, and grabs Amy, then compels her to leap with him through the Eye of Time.
It spits them back out into the Dalek city, where they'd parked the TARDIS. The Eye of Time doesn't seem to be anywhere in sight. Amy asks what happened and the Doctor dismissively explains that they've come to Kaalaan at the time and in the state they left it - the real Kaalaan, how it should be: destroyed. Amy no longer pulses in and out of existence. The Doctor and Amy enter the TARDIS and the Doctor jokes that Amy had wanted to see Ringo Starr, didn't she?
Amy rolls her eyes and they materialize with the TARDIS in proper 1963 just in time to see Sylvia in a red phone booth. She might be late for an appointment, they overhear Sylvia explaining, but it's not the end of the world!
Earth is restored. The Daleks never invaded. The Doctor has saved the day again.