While living as the Soothsayer in the parallel universe created around himself and River Song, the Eleventh Doctor characterised River to Winston Churchill as "hell in high heels." (TV: The Wedding of River Song)
British First Lady Lucy Saxon wore high heels on the Valiant, dancing to Voodoo Child. (TV: The Sound of Drums)
When the Twelfth Doctor asked if Clara Oswald looked taller as she prepared herself for a date, she pointed out that she was wearing heels, to which the Doctor asked if that was because she had to reach a high shelf. (TV: Time Heist) Following her brief possession and metamorphosis by Kali, Clara noted that it was nice to be that tall without "himalayan-sized" heels. (COMIC: The Swords of Kali)
Romana I came to regret wearing high heels, which the Fourth Doctor warned her would not be suitable. By the time she admitted they were not practical, Romana's feet were sore, and she could not go on. She later discarded her shoes entirely, and simply travelled barefoot. In the TARDIS, the Doctor found Romana a pair of more sensible boots, for which Romana was thankful. (TV: The Stones of Blood)
Before scaling a twelve-foot gate that happened to be locked, Tegan lamented to herself about "always wearing heels at times like these". (AUDIO: Hexagora)
While in Monte Carlo in 1966, Erimem wore high heels for the first time. She asked Peri Brown how she could walk in "these torture devices". (AUDIO: The Veiled Leopard)