1963

November

 * 23 - An Unearthly Child First Broadcast (An Unearthly Child Episode 1)


 * 30 - An Unearthly Child Broadcast for second time as many viewers missed the original screening as a result of a power cut


 * 30 - Cave of Skulls First Broadcast (An Unearthly Child Episode 2)

December

 * 06 - The Forest of Fear First Broadcast (An Unearthly Child Episode 3)


 * 13 - The Firemaker First Broadcast (An Unearthly Child Episode 4)


 * 21 - The Dead Planet First Broadcast (The Daleks Episode 1)


 * 28 - The Survivors First Broadcast (The Daleks Episode 2)

March
(Note: Dating and other information is suggested by the Telos novella, "Time and Relative," although it seems to contradict material in "An Unearthly Child" and "Remembrance of the Daleks" suggesting that the TARDIS  arrives in May. See Dating disputes.)
 * Late March - The TARDIS materializes in the junkyard at 76 Totter's Lane, owned by I.M. Foreman, in the Shoreditch area of London, it's navigational systems and chameleon circuit damaged by radiation from the Hand of Omega. While the Doctor attempts repairs and works out a plan for safely disposing of the Hand on Earth, Susan, against his wishes, registers at the nearby Coal Hill School. Britain, meanwhile, is in the grip of an usual cold wave.

April

 * 1- Susan and her new friends discover that the cold wave gripping London is the work of the Cold, an entity which has slumbered since the end of Earth's last Ice Age and which now seeks to conquer the planet and exterminate humanity with its "Cold Knights." At first indifferent to the plight facing the planet, the Doctor is finally convinced by Susan and her friends to intervene, trapping the Cold in a piece of ice which he then takes to Pluto in the distant future before returning back to the  junkyard in 1963. ("Time and Relative")

Late October

 * The Doctor has made arrangements with a local funeral parlor to bury the Hand of Omega in a nearby churchyard. ("Remembrance of the Daleks")


 * Coal Hill School teachers Ian Chesterton and Barbara Wright, curious about their student Susan Foreman, follow her to 76 Totter's Lane, where she apparently lives with her grandfather in a police box in the middle of a junkyard. Forcing their way into the police box, they find themselves inside the Doctor's TARDIS. Fearing they may alert the authorities, the Doctor kidnaps the schoolteachers, taking them on a journey through space and time. ("An Unearthly Child")

November

 * The Nemesis passes by Earth, heralding the assassination of President John F. Kennedy (see below). ("Silver Nemesis")


 * A new science-fiction serial, Doctor ___, begins broadcasting on the BBC. ("Remembrance of the Daleks")


 * The Doctor and Ace arrive in Shoreditch, shortly after two Dalek factions from the future arrive, both seeking the Hand of Omega. The Doctor plays the two factions off against each other, before allowing the winning side, Imperial Daleks led by Davros, to gain the Hand. Unknown to Davros, the Doctor has preprogrammed the Hand to explode Skaro's sun and destroy the Daleks's homewrold once it enters Davros's native time zone, then destroy Davros's ship upon returning to 1963, before finally returning home to Gallifrey.  ("Remembrance of the Daleks;" see also "War of the Daleks")


 * 22 - President John F. Kennedy is assassinated by James Stevens, a journalist who has travelled from the future using a time ring. Stevens is the long-rumored "man on the grassy knoll," who has murdered the President to thwart the Master's plan to sabotage Earth's history and create a timeline in which UNIT and very possibly the Third Doctor never existed. ("Who Killed Kennedy")

Unknown date
The Doctor's companion Nyssa is born on Traken.

Reference

 * Doctor Who: A History of the Universe, by Lance Parkin. Virgin Publishing, Ltd., 1996. ISBN 0-426-20471-9