Dr. Who, his granddaughters Susan and Barbara, and Ian Chesterton are accidentally transported to another planet by the Doctor's new time and space machine, the Tardis. As they explore their surroundings, they spot a distant city and later discover a small container of drugs that they bring aboard the ship. To push the group toward the city in search of the mercury needed to refill a crucial part, the Doctor fakes a leak in a fluid link, a vital component of the Tardis. This cunning move sets the expedition on a dangerous path toward unknown dangers and unexpected alliances.
Upon entering the city, the travelers are swiftly captured by the Daleks, ruthless cyborg invaders who seize the fluid link for examination. The Doctor quickly realizes that the group has contracted radiation sickness, and the drugs they found may be their only chance at survival. While the Daleks observe the captives in secret, they reveal their own predicament: they are trapped inside their metal casings and confined within the city by the same radiation. Their ambition is to escape, destroy all other life, and claim the planet for themselves. Hearing the humans discuss the drugs, the Daleks offer a brutal proposition: bring them the drugs and they will allow the humans enough of a treatment to survive. Susan volunteers for the dangerous mission, the only one still strong enough to undertake it.
Susan eventually reaches the Tardis, retrieves the drugs, and then meets Alydon, the leader of the Thals, a peaceful species that once fought the Daleks in a long-ago atomic war. Alydon provides a second container of anti-radiation drugs, a lifeline for the humans if the Daleks break their promise. Returning to the city, the group learns that the Daleks have discovered the second drug supply but still permit the humans to treat themselves. Susan explains that, according to Alydon, the Thal crops have failed, and the Thals have come to the Dalek city hoping to trade the anti-radiation drug formula for food. Sensing an opportunity, the Daleks decide they no longer need the Thals now that they possess a vital sample of the drug. They coerce Susan into writing a letter to mislead the Thals into thinking food will be provided from the city as a sign of friendship, all while plotting to kill the Thals when they arrive.
A Dalek enters their cell, and the travelers manage to disable it. Free once more, they warn the approaching Thals and escape with them into the jungle. The Daleks then test the Thal anti-radiation drug, only to discover it causes dangerous side effects. In response, they plot to detonate a neutron bomb to raise the planet’s radiation to a level even the Thals cannot endure.
Back at the Thal camp, the Doctor realizes the travelers are effectively trapped on the planet while the Daleks still hold the fluid link. He urges Alydon to mobilize the Thals to help take back the device and save his people, but Alydon initially refuses, insisting the Thals have embraced peace. In a tense moment, the Doctor tricks Ian into taking a Thal woman to the Daleks in exchange for the confiscated component. Horrified, Alydon attacks Ian, then recognizes that the Thals can fight for what they value. With renewed resolve, Alydon, the Doctor, and Susan lead the Thals in a calculated assault on the city. The Daleks, however, repel the frontal assault, and in the chaos, the Doctor and Susan are recaptured.
Meanwhile, Ian, Barbara, and a small group of Thals slip in from the rear and join the main force as the Thals mount a comprehensive effort to rescue the Doctor and Susan. Inside the control room, the Daleks have begun a bomb countdown. In the ensuing struggle, the Daleks inadvertently destroy their own main control console, cutting power to the city and stopping the bomb from detonating.
With the fluid link recovered, the travelers make a decisive escape back to the jungle and depart the planet in the Tardis, taking with them a few Thal capes as tokens of the perilous but hopeful voyage home.
