Cashmere was fine, soft wool, originally that from the Kashmir goat.
The Eleventh Doctor wore a single-breasted frock coat of eggplant purple cashmere with notched lapels when travelling with Clara Oswald; (TV: The Bells of Saint John, etc) most notably when helping to foil the 1562/2013 Zygon Invasion of Earth and when revisting the Fall of Gallifrey on the final day of the Last Great Time War, (TV: The Day of the Doctor) and before and after the Siege of Trenzalore. (TV: The Time of the Doctor) His successor, the Twelfth Doctor, wore it during his first hours. (TV: The Time of the Doctor, Deep Breath)
Romana II wore a double-breasted frock coat and trousers of rose pink cashmere during the Movellan Incident, (TV: Destiny of the Daleks) and when helping to foil the Tremas Master and Autons. (COMIC: Endgame)
The Spy Master wore a single-breasted overcoat of plum purple cashmere with notched lapels during the Kasaavin invasion, (TV: Spyfall) and the Restoration of the Cyber-Empire. (TV: Ascension of the Cybermen|The Timeless Children)