Boater
A boater was a type of hat, usually made of straw.
When the TARDIS arrived in London in 1894 the Eighth Doctor left clothing for Sam Jones to wear which included; a coral-coloured jacket with puffed sleeves, blue bloomers, black Victorian boots and a straw boater-type hat with a coral-coloured band. (PROSE: The Bodysnatchers)
Charles Banham wore a straw boater, slightly lopsided making him look quite the dandy in 1918. (PROSE: Casualties of War)
When the Autons were under the apparent auspices of the Master on Earth in the 1970s they dressed in oversized boaters whilst handing out daffodils. (TV: Terror of the Autons)
Romana II wore a boater when punting in Cambridge. (TV: The Five Doctors)
Whilst being interrogated by Lobos on Xeros utilising thought selection, Lobos thought to probe the First Doctor's mind. The Doctor displayed many confounding images, including him in an Edwardian swimming costume wearing a boater. (TV: The Space Museum)