The Doctor and Nardole are living under the guises of a university professor and his assistant at St. Luke’s University in Bristol. Bill Potts, who works at the university’s canteen, is called to the Doctor’s office, where he notes she attends all his lectures, and Bill eventually becomes the Doctor’s student.

Months pass, and Bill is intrigued by another student named Heather, who has a defect such that it looks like there is a star in her eye. Heather asks her to inspect a mysterious puddle, asking her if she can see what’s wrong with her reflection, but Bill does not notice anything except that her face seems wrong somehow. Bill turns around and Heather has left. Within the puddle, a voice notes its search for a pilot has begun.

Bill meets Heather again, who encourages her to look into the puddle. The Doctor investigates it, and notes that the reflection is not a reflection, but something mimicking them. Bill returns to her flat, and is chased by a moving body of water, which manifests Heather’s likeness. She runs to the Doctor’s office, where water-Heather materializes, forcing him and Bill into the TARDIS. The Doctor moves the TARDIS elsewhere in the university, where he and Nardole check on a vault they have been guarding, thinking whatever is after Bill may be interested in it. Just then, water-Heather appears, causing the trio to return to the TARDIS.

The TARDIS lands again, on the opposite side of Sydney Harbour to Sydney Opera House, where the Doctor admits that he is an alien. The water-Heather arrives again, chasing them. The Doctor takes them to another planet and millions of years into the future, but she finds them again. The Doctor decides to have it chase them through a battle between the Daleks and the Movellans. A Dalek catches the Doctor and Bill, but its shot hits water-Heather. Heather assumes the Dalek’s likeness. The Doctor speculates that when the substance that took possession of Heather found her, it found someone who wanted to leave. Bill convinces the creature to let her go, and it melts away.

The Doctor and Bill return to his university office, where he attempts to wipe Bill’s mind but she stops him. He says that he has promises to keep, that he is in disguise and no-one should know who he is. As Bill leaves the grounds, she finds the Doctor waiting for her with the TARDIS, having changed his mind. Bill agrees to travel with the Doctor.

Classic Doctor Who Homework:
The War Machines

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