14 January 1934: birth of Richard Briers, who played the Chief Caretaker in Paradise Towers (Seventh Doctor, 1988) and Henry Parker in A Day in the Death (Torchwood, 2008).
14 January 1963: birth of Adjoah Andoh, who played Sister Jatt in New Earth (Tenth Doctor, 2006) and Martha's mother Francine Jones in the 2007 series 3.
14 January 1965: birth of Jemma Redgrave, who played Kate Stewart (not my cousin) in several Eleventh and Twelfth Doctor stories.
14 January 1974: death of Paul Whitsun-Jones, who played the Squire in The Smugglers (1966) and the Marshal The Mutants (1972).
14 January 2005: death of Jack Kine, visual effects designer whose photograph is used on screen for the facist leader of the parallel Britain in Inferno (Third Doctor, 1970).
14 January 2016: death of Robert Banks Stewart, author of both Terror of the Zygons (Fourth Doctor, 1975) and The Seeds of Doom (Fourth Doctor, 1976).
14 January 1967: broadcast of first episode of The Underwater Menace. The Doctor and friends land on a marine volcano around 1968. They escape sacrifice to the god Amdo, but Polly is threatened with transformation into a fish creature.
14 January 1974: broadcast of second episode of Underworld. The Doctor, Leela, Jackson and the crew explore the planetoid around the P7E.
iii) date specified in canon
14 January 2594: Benny Summerfield turns up on the planet of Tyler's Folly (in Lawrence Miles' 1997 novel Down).