A flat cap was a type of hat.
Following his regeneration, the Third Doctor tried on a flat cap. Upon looking in a mirror, he decided against wearing it. (TV: Spearhead from Space [+]Loading...["Spearhead from Space (TV story)"])
Romana I wore a flat cap of tartan on her first visit to Earth. (TV: The Stones of Blood [+]Loading...["The Stones of Blood (TV story)"])
Professor Jericho and Dan Lewis wore flat caps of herringbone-tweed during the early 1900s. (TV: Survivors of the Flux [+]Loading...["Survivors of the Flux (TV story)"], The Vanquishers [+]Loading...["The Vanquishers (TV story)"])
Wilfred Mott was wearing a flat cap of houndstooth tweed when the Fourteenth Doctor and Donna Noble returned to Camden Market from the edge of the universe. (TV: Wild Blue Yonder [+]Loading...["Wild Blue Yonder (TV story)"])