- You may be looking for Doctor Who parodies.
A great number of the video and audio-based pastiches of the Doctor and Doctor Who were produced during what is often called the "Wilderness Years", the period when Doctor Who was not being produced in a video format post-1989 to 1996 and post 1996 to 2005.
There have also been a few in-universe instances of Doctor Who parodying itself. The series known as "Professor X" is a broad pastiche of the Doctor and Doctor Who; in the Virgin New Adventures novel No Future Bernice Summerfield even briefly visited a fictional universe where she met Professor X himself and travelled in his "TASID", a ship that looks like a pillar box and can travel through time and space. In the later Virgin New Adventures Head Games a fictional version of the Doctor generated from the Land of Fiction appears, known as Dr. Who, broadly being a pastiche not just of the Doctor, but also of Dr. Who of the 1960s Dalek movies.
During the Classic Series original broadcast and setting up Big Finish, Nicholas Briggs played the Doctor in a series of fan audio stories. Some of these scenarios were reused and adapted for some of Big Finish' main range.
BBV Productions in particular created a number of pastiches of the Doctor for their productions in both audio and video, in particular "the Stranger" played by Colin Baker and "the Professor" (later "the Dominie") played by Sylvester McCoy.
"The Stranger" was a series of video dramas featuring Colin Baker as the title character, originally a loose pastiche of the Doctor. One episode, More Than a Messiah, was even based upon a fan-written Doctor Who audio drama. Nicola Bryant appeared in the first three stories as Miss Brown, a pastiche of her Doctor Who character Peri Brown; however "Miss Brown" had an English accent rather than Peri's American. The roles this pair played was loosely similar to their roles in Doctor Who, but beginning with the fourth adventure of "The Stranger" BBV decided to explain away the Stranger as a different character, named Solomon, with an entirely different past.
BBV also produced a series of audio stories featuring "The Professor", who later was known as "the Dominie" due to legal reasons, played by Sylvester McCoy, along with Sophie Aldred playing a character called "Ace" which was later changed to "Alice."
Like "The Stranger" this was another series of thinly veiled versions of the Seventh Doctor and Ace. These stories were scripted by a number of writers who around their time of production had written Doctor Who stories or went on to write for Doctor Who in one medium or another such as; Robert Shearman (under a pseudonym), Mark Gatiss and Nigel Fairs.
In the "Cyberon" series of audio adventures, Nicholas Briggs, who had played "the Doctor" in a series of fan audio series made by Audio Visuals, played a character called "The Wanderer" or "Fred" in the audio stories Cyber-Hunt and Vital Signs. Like "the Stranger" and "the Dommie" this was a loose interpretation of "the Doctor" this time based on Briggs' own portrayal in the Audio Visuals series.
BBV Productions did not just attempt pastiches of the Doctor. In 1999 two audio stories in a series called Adventures in a Pocket Universe were produced that featured K9 and "The Mistress", played by John Leeson and Lalla Ward. While the producers of these audios were able to licence K9, they couldn't licence Romana. As a result, she was never referred to by this name. Later, when Big Finish Productions obtained a full licence to produce Doctor Who-based audio dramas, Ward performed the character as Romana.
Other Doctor Who pastiches
- The Marvel Universe had Professor Justin Alphonse Gamble and his enemies the Incinerators. Notably, Professor Gamble had stolen a time machine from the Time Variance Authority. Later Marvel and Marvel UK stories introduced WHO, or the Weird Happenings Organisation, led by Doctor Alistaire Stuart along with his sister, Brigadier Alysande Stuart. (They are obviously named after Alistair Gordon Lethbridge-Stewart.) This was originally the creation of British-born Marvel writer Chris Claremont. During the course of his career, he made many references to Doctor Who in his scripts.
- The Wildstorm comic book The Establishment featured Mister Pharmacist, who resembled a much darker and sinister version of the Fourth Doctor. He worked alongside a team of super-secret agents based on other characters from British fantasy and adventure television series. The Establishment made many other allusions to this genre and to British pulp fiction.
- Grant Morrison's The Invisibles featured surgically altered drone henchmen known as the Cyphermen.
- In the Wallace and Gromit comic "The W Files" there is a spoof of the Brigadier, Sergeant Benton and UNIT.
- Alan Moore features The First and Second Doctors as well as Doctor Omega in his League of Extraodinary Gentlemen.
- The ITV children's drama series Press Gang (written by Steven Moffat) in one episode features Colonel X, an eccentric, suave and mysterious children's television hero. Colonel X and the actor who played him, John England, were both portrayed by Michael Jayston who also played the Valeyard on Doctor Who.
- Professor Paradox, a heroic time travelling scientist from the American animated series Ben 10: Alien Force.
- In the BBC soap opera Doctors, Seventh Doctor actor Sylvester McCoy played Graham Capelli, who had played a 1980s children's television character called "The Lollipop Man". At one point, Capelli is mistaken for Jon Pertwee.
- The NBC comedy Community features a show-within-a-show called Inspector Spacetime, which follows the eponymous Inspector and his associate Constable Reggie as they travel through time and space in their red phone booth, fighting enemies such as the "Dalek-like" Blorgons. A British programme, Inspector Space Time is said to have begun in 1962, thus making it the oldest sci-fi show on television. A brief glimpse of the opening credit sequence is very like that of Doctor Who during the Ninth/Tenth Doctor era.
- This show-within-a-show now has a pastiche of itself in the form of a web series created by Travis Richey, the actor who portrays "the Inspector". After Richey attempted to start an Inspector Spacetime web-series, using Kickstarter to help fund the show, lawyers representing Sony requested the production be cancelled. Instead, the show was renamed to Untitled Webseries About A Space Traveler Who Can Also Travel Through Time, and the appearance of "the Inspector" was altered.
- Doctor Omega was the main character of the 1906 French science fiction novel Le Docteur Omega by Arnould Galopin. After Doctor Who nonfiction writer Jean-Marc Lofficier discovered the character and noticed the similarities between him and the First Doctor, Lofficier and his wife, Randy, republished the book in an English translation. They gave it a new cover, similar to that of Chris Achilleos' for Doctor Who in an Exciting Adventure with the Daleks, with an introduction by veteran Who writer Terrance Dicks. Lofficier added lines suggesting that the novel told adventures of the Doctor shortly before An Unearthly Child, with the Doctor having taken a brief leave of absence from his grand-daughter, Susan Foreman.
- The Stranger is a 1997 erotic novel by Portia Da Costa. It was published by Virgin Books after they lost the rights to the series under their Black Lace range and featured an amnesic Eighth Doctor. The character Claudia was then mentioned as a companion in the BBC Eighth Doctor Adventures novels Father Time and The Gallifrey Chronicles by Lance Parkin.