The TARDIS lands in London, near the Post Office Tower. The Doctor is unsettled by a sensation of a strange energy nearby. Visiting the newly completed Tower, the Doctor and Dodo meet Professor Brett, the creator of WOTAN (Will Operating Thought ANalogue), an advanced problem-solving computer that thinks for itself. Curiously, WOTAN even knows what the word 'TARDIS' stands for. In four days' time, on C-Day, WOTAN will be linked to other major computers to take them over, including those of the White House, Cape Kennedy and the Royal Navy.
Dodo goes with Polly, Brett's secretary, to the local Inferno nightclub, where they meet Able Seaman Ben Jackson, while the Doctor attends a Royal Scientific Club meeting about WOTAN, lead by Sir Charles Summer. Before Brett can depart the GPO Tower for the meeting, he is hypnotised by a humming noise emitted by WOTAN. He then fetches Krimpton, an electronics colleague, from the meeting and takes him to WOTAN, who is likewise possessed by the computer. Major Green, the chief of security in the Tower, is also taken over, and sends WOTAN's control signals to Dodo at the nightclub via telephone. Going to the tower, WOTAN tells her "Doctor Who is required. Bring him here."
WOTAN has concluded that mankind cannot develop the world any further, and intends to take over using an army of War Machines - mobile computers like itself. Using its hypnotic control, WOTAN enlists a workforce to construct 12 War Machines around London, which is the first capital to become controlled. One of these machines is built in a warehouse in Covent Garden, close to the Inferno nightclub. Dodo, the Doctor, Ben and Polly leave for Sir Charles' residence, where the Doctor has been invited to stay, in a taxi that drops off a tramp by the nightclub. Looking for a place to sleep, the tramp discovers Brett and a workforce building Machine 3 in the warehouse. The tramp is caught, and killed when he tries to escape.
The next day, Dodo manages to get the Doctor to telephone Brett at the GPO Tower, and he is nearly possessed by WOTAN. Thinking the Doctor is now controlled, Dodo gives herself away by revealing that the War Machines are being "constructed in strategic points in London". The Doctor breaks WOTAN's hypnotic control over her, and she is sent to stay with Sir Charles' wife in the country to recover.
When Polly fails to show up to a luncheon with Ben, the Doctor sends the lad to investigate the area around the nightclub, after reading about the death of the tramp in the newspaper. Ben also discovers the War Machine in the warehouse, now fully assembled and being tested under Major Green's supervision. Ben is detected by the Machine, and caught by the now hypnotised Polly. However, Ben is spared when Polly states that "WOTAN requires all the slave labour we can find". While working with the others, Ben learns that the 12 War Machines are to attack at noon the next day. He escapes, although seen yet not stopped by Polly, and alerts the Doctor and Sir Charles. Polly is sent back to the Tower to be punished by WOTAN.
Under Sir Charles' instruction, an army taskforce investigates the warehouse, but their weapons are somehow disabled by the War Machine. They are forced to retreat, but when Doctor stands defiantly before the Machine as it emerges from the warehouse, it stops - it had not been completely programmed. With the deactivation of Machine 3, the workmen, including Major Green, are released from its control. Examining the Machine's programming, the Doctor learns that the 11 others have been built across London, and are meant to attack at noon today. Soon after, there are reports of another War Machine - Machine 9 - taking to the streets, having gone rogue while it was being tested. With the help of the army, the Doctor traps the Machine in an electromagnetic forcefield - paralysing it - and reprogrammes it to destroy WOTAN. Ben goes to the GPO Tower ahead of Machine 9, and drags Polly out of the WOTAN room as the Machine enters and attacks the immobile computer. Krimpton is killed, but WOTAN is destroyed before it can give the order for the other 10 War Machines to commence their attack - and Brett and all the others who have been hypnotised return to normal.
Ben and Polly meet the Doctor at the TARDIS, to explain that Dodo has decided to stay in London. The Doctor thanks them and heads into the police box - followed by Ben and Polly, who enter the TARDIS with the intent to return Dodo's key, which the Doctor dropped earlier. They are then suddenly whisked off into time and space...