Flat cap

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: )

Romana I wore a flat cap on her first visit to Earth. (TV: )

Wilfred Mott wore a flat cap of houndstooth tweed when he reunited with Donna Noble and the Doctor in his fourteenth incarnation. (TV: )