Cross-dressing

Cross-dressing was the act of wearing items of clothing culturally associated with another gender.

Rose Tyler, a human from 2000s London, was scandalised to find that a Slitheen impersonating the Ninth Doctor was a girl, Slist Fayflut Marteveerthon Slitheen. Though Slist saw nothing of it, Rose made a point to note that she was a "cross-dressing Slitheen" for wearing a synthetic skin suit of the male Doctor. Rose quipped that Jack Harkness would "love [her]" for that. (COMIC: Doctormania)

Similarly, the matriarch of the clan Klep-Clotch Slitheen wore a suit made from the skin of Sir Edward Scott Cameron. (AUDIO: Death on the Mile)

The Second Doctor disguised himself as an old woman while hiding from the British in 18th century Scotland. (TV: The Highlanders)

The Third Doctor disguised himself as a cleaning lady while infiltrating Global Chemicals. (TV: The Green Death)

Several incarnations later, the Thirteenth Doctor noted that she hadn't shopped for women's clothing in a while. After regenerating from her male predecessor, she remained in his clothes for an extended period of time before acquiring an outfit of her own from a charity shop. (TV: The Woman Who Fell to Earth)

While living with Panda in the 2000s, Tom once dressed up in drag for Halloween, and called himself "Eartha Wydenfire". (PROSE: The Golden Hendecahedron)

During the War in Heaven, dressing up as women was a tactic used by male Great House agents to infiltrate opposing military forces. Robert Scarratt believed that agents with transgender orientations would be "organically and symbolically" better able to handle the alter-time states of their opponents. (PROSE: The Book of the War)

Behind the scenes
Tenth Doctor actor David Tennant cross-dressed as he played the role of a female companion to the Doctor, played by, in a comedic sketch as part of an episode of Channel 4's.

Every actor in the role of the Doctor except for William Hartnell and Paul McGann has cross-dressed as part of a role in a TV show or film, while Patrick Troughton, Jon Pertwee, and Jodie Whittaker have done so on Doctor Who itself.