Daleks: Invasion Earth (in-universe)

Daleks: Invasion Earth was a film which starred Peter Cushing as a character named "Dr. Who", evidently featuring a Dalek invasion of Earth. It was one of two films which saw Cushing's Doctor Who confronting the Daleks, both of which were collected as VHS cassettes within UNIT's Black Archive. The two movies were very much enjoyed by the Tenth and Eleventh Doctors, who pitched a third one to Cushing on the phone. (PROSE: The Day of the Doctor)

The Third Doctor had previously watched the pair of films in the 1970s, the latter of which featuring Cushing's return to the role. One scene involved antics with a food machine, something that caused the Doctor to tear up in laughter. (PROSE: A Visit to the Cinema)

Behind the scenes
In real life, Daleks' Invasion Earth 2150 A.D. is a 1966 Dr. Who film starring Peter Cushing, adapted from The Dalek Invasion of Earth and following the 1965 production Dr. Who and the Daleks.