"You can't rewrite history - not one line!"

In the spring of 1963, The TARDIS lands in a junkyard at 76 Totter's Lane in the Shoreditch area of London, England, disguising itself as a Police Call Box (which would normally be found on the street). The junkyard is owned by the mysterious I.M. Foreman, and Susan adopts his last name when she enrolls at Coal Hill School. During the five months The Doctor and Susan spend in London, The Doctor makes repairs to the TARDIS and also studies the Hand of Omega, which he plans to bury on Earth. He is somewhat reclusive, although he does spend time in a neighborhood cafe, becoming friendly with its owner (Remembrance of the Daleks). Susan enjoys school and fits in fairly well, but makes several statements which betray her advanced knowledge, or show her unfamiliarity with current events. Her history teacher, Barbara Wright, grows curious, and she discusses Susan with science teacher Ian Chesterton, who's noticed similar oddities. Together they go to Totter's Lane and see Susan enter the junkyard, but there's no sign of her when they follow. They discover the police box, which emits a hum of power. Their inspection is interrupted by The Doctor, who attempts to drive them away. Susan opens the TARDIS door, and the teachers rush in, finding themselves in a futuristic control room. The Doctor, worried about what they might tell the authorities, tells Susan that they must leave London, and when she refuses he activates the ship's controls. The TARDIS lands in prehistoric times and the ship's chameleon circuit fails, causing it to remain in its police box guise. While Ian and Barbara attempt to cope with their new reality, The Doctor explores. A caveman from a tribe which has lost the secret of fire sees him light his pipe, and captures him. Unfortunately The Doctor has used his last match. The others arrive, and are captured and forced to make fire. Eventually Ian succeeds, and Susan suggests setting fire to skeletons left in the cave where they are imprisoned as a distraction. The travelers manage to stay ahead of the pursuing cavemen and make their way back to the TARDIS. Following this, the ship lands on an alien world and the travelers fail to notice the warning of the ship's radiation meter.

The TARDIS has arrived on the planet Skaro, where The Doctor discovers a city he wishes to explore. He forces the others to help him by claiming that the ship has run out of mercury, a vital component used in its fluid links. The crew are captured by the Daleks, a race of beings who've encased themselves in robotic shells because of mutations caused by fallout from a war with the Thals. The Daleks are restricted to their city because they require the static electricity from its metal floors to move, and they are suffering from radiation sickness, which is also affecting the TARDIS crew. The Thals have drugs for this, and Susan is allowed to leave to obtain them. The peaceful Thals wish to exchange medicine for food, but the Daleks set a trap and kill their leader, Temmosus. The Doctor and his companions escape with the Thals, but The Doctor has left the fluid link in the city. He and Ian convince the Thals to fight, not just because they need the aliens' help, but because the Daleks will destroy all of them if they don't defend themselves. Together they defeat the Daleks, apparently killing them by cutting off their power source, and the TARDIS crew are hailed as heroes. The parting gifts they receive from the Thals include a scroll granting The Doctor the "freedom of the city of Skaro" (Robot).

The TARDIS lands in the tomb of Yetaxa, the high priest of the Aztecs, who are a particular interest of Barbara's. She tries on his bracelet, and is hailed as his reincarnation when the group leaves the tomb. Barbara attempts to change the course of history by ending the Aztec sacrifices, despite The Doctor's warnings that it is impossible for her to do so. The Doctor also has to solve the problem of getting back into the tomb, which sealed behind them, and befriends Cameca, a revered elderly lady whom he thinks can help him. Despite the fact that his ignorance of the local customs gets him engaged to the lady when he shares a ritual cup of chocolate with her, he manages to get the information, and the crew escape by using a wheel and pulley, which the Aztecs never invented. Although he considers leaving it behind, The Doctor decides to keep a brooch which Cameca gave him as a memento of their relationship.

The TARDIS arrives on a spaceship orbiting the Sense-Sphere, and finds that its crew are held captive by the Sensorites, an alien race with telepathic abilities. Susan communicates with them (The Doctor's telepathic skills have weakened with age, and he denies possessing such abilities) and she learns that the Sensorites are afraid of being exploited by the humans, who have discovered molybdenum on their planet. The travelers also learn that many Sensorites have died from an illness which they blame on a previous Earth expedition. The Doctor discovers that they have actually been poisoned, and after he finds an antidote, he and Ian learn that three surviving members of the earlier expedition are responsible. The travelers depart and the captain of the spaceship promises to preserve the Sensorites' secrets.