In no particular order:
- Elizabeth I (several mentions & appeared briefly in "The Shakespeare Code");
- Elizabeth II (he had tea with her, according to Elizabeth X, "Liz Ten");
- Elizabeth X ("The Beast Below");
- Victoria ("Tooth and Claw");
- Richard I, "the Lionheart" ("The Crusade");
- Athelstan (mentioned in "Planet of the Dead");
- Charles II ("The Impossible Astronaut", opening sequence);
- Henry VIII ("The Power of Three");
- an android (Kamelion) impersonating John but not the real King John ("The King's Demons");
- Henry XII (mentioned in "The Beast Below").
These are from TV stories. He has met others in non-TV stories.