Doctor Who pastiches

A number of unauthorized versions of Doctor Who and of the Doctor have appeared.

Partial list

BBV Productions introduced Colin Baker as "the Stranger", originally a loose pastiche of the Doctor, who developed into a more original character. Appearing in the first three films was Nicola Bryant as Miss Brown, a pastiche of Peri Brown.
BBV also produced a comedy short film, Do You Have a Licence to Save This Planet? a parody in which Sylvester McCoy plays "The Foot Doctor". The film includes numerous references to Doctor Who as well as original alien races from the show such as Sontarans, Autons and a bastardized version of Cybermen, the Cyberons. The film poked fun at the fact that BBV and others were able to use monsters and other characters from Doctor Who, but never the Doctor himself.

BBV introduced Sylvester McCoy as "the Professor", later (for legal reasons), "the Dominie", with Sophie Aldred as "Ace", later Alice. The audios featured scripts by, among others, Robert Shearman (under a pseudonym), Mark Gatiss and Nigel Fairs.
The Wanderer or Fred, played by Nicholas Briggs in the BBV audio adventures Cyber-Hunt and Vital Signs is loosely based on the Doctor as portrayed by Briggs in the Audio Visuals fan audio series. In Cyber-Hunt, he comes up against Cyberons.
Lalla Ward and John Leeson reprised their roles as Romana and K-9, respectively, for a series of audio dramas called The Mistress and K-9. While the producers of these audios were able to licence K-9, they couldn't licence Romana, thus she was never referred to by this name. Later, when Big Finish obtained a full licence to produce Doctor Who-based audio dramas, Ward was once again able to perform the character as Romana.

The Marvel Universe had Professor Gamble and his enemies the Incinerators. Later Marvel and Marvel UK stories introduced WHO, or the Weird Happenings Organization, 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 Marvel writer and Anglophile, Chris Claremont, who, during the course of his career, incorporated several brief references to Doctor Who into 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.

The Doctor Who Universe itself has a pastiche version of Doctor Who, called Professor X. Bernice Summerfield briefly visited that fictional universe and met Professor X during No Future.