Special Constable Tom Campbell encounters a jewellery shop burglary. Running to what appears to be a police box to summon backup, he enters the Tardis, a time and space machine operated by its inventor Dr. Who, his niece Louise and granddaughter Susan, as it departs for the future. Arriving in London, 2150 A.D., they find that Daleks have invaded the Earth. Some survivors have become resistance fighters, while captives are either turned into brainwashed 'Robomen' servants, or forced to labour at a mine in Bedfordshire.
On the Dalek spaceship, Dr. Who and Tom are captured and imprisoned, while a rebel, Wyler, takes Louise and Susan to a London Underground resistance base. There they meet fighters including David and Dortmun, who plans to bomb the Dalek ship using rebels disguised as Robomen. On the ship, Dr. Who and Tom avoid being robotised when the rebels, including David, Wyler and Louise, attack. Dr. Who escapes with David, while Tom and Louise become trapped on the spaceship. After the attack fails, Wyler returns to the base and informs Dortmun and Susan that Dr. Who escaped. They decide to hide in London's outskirts until the rebels can regroup. Susan writes a message about their intentions for Dr. Who, then they commandeer a van. Dortmun is killed by a Dalek patrol, and Wyler and Susan have to abandon the vehicle just before it is destroyed.
Dr. Who and David manage to return to the now deserted underground station. Failing to see Susan's message, they assume that Wyler, Dortmun and Susan have gone to Bedfordshire to investigate the mining operation and decide to follow them. Hiding on the Dalek spaceship, now bound for the mine, Tom and Louise reunite. When the craft lands they escape from it. Finding themselves in the mining complex, they are saved from a Roboman by one of the slave-workers, who hides them in a tool shed.
Wyler and Susan shelter in a cottage, occupied by a mother and daughter. Susan convinces Wyler that Dr. Who would head for the Bedfordshire mine, and that they must follow. The daughter then leaves on an errand, but returns with Daleks who capture Wyler and Susan and take them to their mine control centre. Near the mine Dr. Who and David are confronted by black marketeer Brockley, who agrees to smuggle them into the complex. By chance, he leads them to the tool shed where Tom and Louise are hiding. They are joined by a prisoner, Conway. He reveals that the Daleks intend to drop a bomb into their mineshaft, to destroy the Earth's core and replace it with a device enabling the planet to be piloted like a giant spacecraft. Stolen plans show an old shaft leading to a convergence between the planet's magnetic poles. Realising that an explosion at this point would release enough energy to destroy the metallic Daleks, Tom and Conway agree to try deflecting the bomb while Louise and David go to help evacuate the prisoners from the mine. Brockley leaves, refusing to get involved, but returns with a group of Daleks. As Dr. Who is led away the Daleks fire on Brockley, killing him.
Tom and Conway enter the mineshaft but are discovered by a Roboman. During the ensuing fight Conway and the Roboman fall to their deaths. Tom uses old timbers to create a deflecting ramp, then leaves. Dr. Who is taken to the mine control room and meets Wyler and Susan. He seizes the radio link to the Robomen and orders them to turn against their masters. The Robomen and Daleks fight, while everybody else flees from the mine. The Daleks quickly defeat the rebellion and release their bomb into the shaft, but the device is deflected and detonates at the pole convergence. The Daleks are pulled into the Earth's core and destroyed, while their spaceship crashes onto the mine and explodes.
As the travellers prepare to return to the present in Tardis, Tom asks to be taken back to a few minutes before the burglary occurred. Upon arrival, he knocks out the thieves and drives them away in their getaway car, heading for the police station and anticipating a promotion.
