Even though the popular science fiction British series Doctor Who works with the theme of time travel, it does share similarities with the real world. And it also likes to use real historical figures. The Doctor has the power to travel not only into the future but back in time as well. As a result, various regenerations of the Doctor met multiple historical figures.
Some of them turned out to be his friends, others weren't so excited about the Time Lord. But despite the fact that Doctor Who has already portrayed multiple historical figures, there are still some who haven't been on the show and who the fans would like to see one day.
5 Edgar Allan Poe
As one of the first major horror and crime writers, Edgar Allan Poe set the tone for many future writers to come. He also led an interesting, albeit not always easy life. Considering the overall atmosphere of his literary work, including Poe in Doctor Who would most likely make for a memorable horror episode.
Plus, it wouldn't be the first time the Doctor would work with a famous writer, as he met Charles Dickens and Agatha Christie, to name just two, and helped them solve mysteries. There'd be another advantage to doing an episode about Edgar Allan Poe. It would allow the show to bring back the frightening ravens who were responsible for killing Clara (sort of)... because the name of Poe's most famous piece of work is The Raven.
4 Leonardo Da Vinci
Meeting Leonardo da Vinci would give the Doctor the opportunity to measure his intellect against one of the most brilliant artists and inventors of all time. Plus, Leonardo da Vinci lived in Italy and France in the early Renaissance days, which could make for impressive settings.
As for the plot, the Doctor and da Vinci could, for example, work together to help the Doctor escape this time period after the Doctor had been stranded there. If any historical figure could build a functioning time machine, it's Leonardo da Vinci. Meeting the Doctor would also help explain how da Vinci was ahead of his time...simply because he met a time-traveling alien and realized that everything was possible. Of course, the Fourth Doctor has already met Leonardo da Vinci, but that's been a while back, so da Vinci could very well make a comeback.
3 Georges Méliès
The history of cinema isn't as long as the history of literature, but it still has some remarkable figures that could bring something new to Doctor Who. Georges Méliès was the first major sci-fi and horror director who created dozens of movies belonging to this genre, including his most iconic work, A Trip to the Moon (1902). If Méliès and the Doctor met, the Doctor could very well be astonished by the director's imagination.
The pleasant visit could turn into something more adventurous, for example, if the characters from Méliès' movies suddenly became real or if he and the Doctor were trapped in one of Méliès' movies and had to find their way out. Plus, who's to say Méliès couldn't have gotten the idea for his space adventures from the Doctor. Méliès has previously appeared in an audio story Deleted Scenes, but he has yet to make a live appearance.
2 J. R. R. Tolkien
Doctor Who likes to give space to the greatest names of British literature. And as far as the fantasy genre is concerned, there's no one greater than J. R. R. Tolkien, the author of The Lord of the Rings. Tolkien was a well-educated and intelligent man, something he and the Doctor share. Considering his importance for fantasy and literature in general, it's only a matter of time before Tolkien appears in one form or another in Doctor Who.
The Doctor might have a hard time dealing with something truly magical and Tolkien would be the perfect person to assist him since his books are full of magic and creatures that aren't supposed to exist. That's a description that also fits the Doctor, in a way. And if Tolkien and the Doctor got to meet a talking dragon in their mutual episode, even better.
1 Alan Turing
The show likes to highlight the impact of people who have been misjudged by the world or even persecuted. Alan Turing fits in the second category, and if he appeared in Doctor Who, it wouldn't be the first episode focused on World War Two. Turing was instrumental in breaking the Enigma code which gave an advantage to the Allies and quite possibly shortened the war. Doctor Who could feature an episode in which somebody breaks time and the Doctor has to go back in time and save Turing or else the war will go on. It could also address the fact that despite Turing's war work, he was persecuted due to his sexual orientation (he was a homosexual), and that led to his premature death.
What could make Turing's appearance even more extraordinary would be if Benedict Cumberbatch took on the part! Cumberbatch had already played Turing once in the Oscar-winning movie The Imitation Game (2014) and before making it big in Hollywood and being cast in the MCU as Doctor Strange, he was no stranger to appearing in British TV shows. What's more, fans once pushed for Cumberbatch to become the new Doctor, so his presence in the show would no doubt please many of them, even for a single episode or two!