Velvet was a soft fabric used to make clothes, curtains, and furniture.
The Doctor
The Eighth Doctor wore double-breasted frock coats of velvet done in forest green, (TV: Doctor Who) navy blue, (COMIC: Dreadnought) olive green, (COMIC: Ophidius) or dark brown. (PROSE: The Year of Intelligent Tigers) He also wore a single breast waistcoat of mustard yellow velvet with a double breast overcoat of bottle green moleskin. (COMIC: The Pictures of Josephine Day)
The Third Doctor wore many smoking jackets of velvet coming in navy blue with a rolled collar, (TV: Doctor Who and the Silurians) maroon with a rolled collar, (TV: Terror of the Autons) rust orange with a notched collar, (TV: The Curse of Peladon) olive green with a notched collar, (TV: Carnival of Monsters) plum purple with a notched collar, (TV: Planet of the Daleks) petrol blue with scarlet piping on the notched lapel, (TV: The Green Death) aquamarine with a notched collar, (TV: Invasion of the Dinosaurs) emerald green with a notched collar, (TV: The Monster of Peladon) charcoal with a notched collar, (TV: Planet of the Spiders) and burgundy with a rolled collar. (TV: The Five Doctors)
The Fourth Doctor wore a trenchcoat of plum velvet when he and Romana II foil Tryst's conversion of Mandrels into Vraxoin. (TV: Nightmare of Eden)
The Eleventh Doctor wore single-breasted waistcoats of velvet, done in plum (TV: The Snowmen) or black. (TV: Nightmare in Silver)
The Twelfth Doctor wore a single breast frock coat of black velvet. (TV: The Pilot)
Others
Sarah Jane Smith wore sapphire blue velvet jeans when she and the Third Doctor helped to save Peladon from Azaxyr and Eckersley. (TV: The Monster of Peladon) She also wore a navy velvet blazer similar to the Third Doctor's when she met the Mona Lisa. (TV: Mona Lisa's Revenge)
The Master wore a high-collar tunic and black velvet gloves when he stole Tremas's form. (TV: The Keeper of Traken-The Fiver Doctors) During his bald incarnation, he wore a charcoal velvet blazer. (AUDIO: Master of the Daleks)