An ascot tie was a necktie, similar to a cravat; worn over or under the collar of a shirt.
Worn by the Doctor
The First Doctor wore a cream ascot tie with ivory stripes when he met Vicki, (TV: The Rescue) and when helping the Menoptera in defying the Animus and Zarbi. (TV: The Web Planet)
The Eighth Doctor wore ascot ties of dupioni under the collar of his white shirt; one in flaxen yellow, (COMIC: The Pictures of Josephine Day) eggplant purple, (COMIC: A Matter of Life and Death) dark teal, (COMIC: The Lost Dimension) azure blue, (AUDIO: He Kills Me, He Kills Me Not-Mutually Assured Destruction) ebony black (AUDIO: Meanwhile, Elsewhere-Previously, Next Time) or midnight blue. (TV: The Night of the Doctor) His war successor wore the midnight blue ascot tie for some time. (TV: The Night of the Doctor; AUDIO: Light the Flame; WC: Doctors Assemble)
The Sixth Doctor wore an ivory ascot tie with ebony black polka dots under the collar of his salmon pink shirt when he reunited with Peri Brown on the Memory TARDIS. (TV: Vengeance on Varos)
The Ninth Doctor wore an ascot tie of burgundy brocade in 1912 Southampton, (TV: Rose)
The Curator, while in the form of an older Fourth Doctor, wore ascot ties under the collars of his shirts done in navy and crimson paisley, (TV: The Day of the Doctor) or plain burgundy. (COMIC: The Then and the Now)
Worn by Companions
Harry Sullivan wore a plum purple ascot tie under the collar of his sky blue shirt during his travels with the Fourth Doctor. (TV: Robot, The Ark in Space, The Sontaran Experiment, Genesis of the Daleks, Revenge of the Cybermen)
Worn by Others
Captain Cook, an intergalactic explorer, wore an ascot tie of burgundy and beige paisley under his shirt's collar. (TV: The Greatest Show in the Galaxy)
Redvers Fenn-Cooper wore an ascot tie of burgundy and gold paisley under the collar of his ivory shirt. (TV: Ghost Light)
Oscar Botcherby wore an ascot tie of bronze paisley under his shirt's collar when he and Anita met the Sixth Doctor, Peri Brown, and Jamie McCrimmon after seeing Sontaran Group Marshal Stike's scoutship fly over. (TV: The Two Doctors)
Flores wore an ivory ascot tie under his white shirt's collar when he met the Seventh Doctor, Ace, and Isomorph Cybermen on England during the 1988 Cyber-Invasion of Earth. (TV: Silver Nemesis)
The Valeyard wore a copy of the Eighth Doctor's midnight blue ascot tie. (AUDIO: The War Valeyard)
The Half-Face Man wore a burgundy ascot tie during the 1890s. (TV: Deep Breath)