4 February 1919: birth of Peter Butterworth, who played the Meddling Monk in The Time Meddler (First Doctor, 1965) and The Daleks' Master Plan (First Doctor, 1966).
4 January 1933: birth of James Mellor, who played Sean Flannigan in The Wheel in Space (Second Doctor, 1968) and Varan the Bad Native in The Mutants (Third Doctor, 1972).
4 February 1948: birth of Stephen Wyatt, as far as I know the only alumnus of Clare College, Cambridge, to have written for Who (Dan Zeff, a contemporary of mine, has directed); he wrote Paradise Towers (Seventh Doctor, 1987) and The Greatest Show in the Galaxy (Seventh Doctor, 1988).
4 February 1951: birth of Dez Skinn, founding editor of Doctor Who Magazine.
4 February 1980: death of David Whitaker, the first script editor of Doctor Who (from An Unearthly Child to The Dalek Invasion of Earth) and writer of The Rescue (1964), The Crusade (1965), The Power of the Daleks (1966), The Evil of the Daleks (1966-67), The Enemy of the World (1967-68), The Wheel in Space (1968) and The Ambassadors of Death (1970); also of the 1965 stage play, The Curse of the Daleks, and of two of the first three novelisations, Doctor Who in an Exciting Adventure with the Daleks (1964) and Doctor Who and the Crusaders (1965).
ii) broadcast anniversaries
4 February 1967: broadcast of fourth episode of The Underwater Menace. The Doctor and friends prevent Zaroff's plan but Atlantis is flooded and destroyed.
4 February 1978: broadcast of first episode of The Invasion of Time. The Doctor returns to Gallifrey and has himself inaugurated as President, but collapses on contact with the Matrix.
iii) date specified in-universe
4 February 1814: the Twelfth Doctor and Bill Potts arrive in Regency era England and discover that a creature under the Thames is eating people (Thin Ice, 2017).