1963

March
(Note: Dating and other information is suggested by the Telos novella Time and Relative, although material in An Unearthly Child and Remembrance of the Daleks suggests that the TARDIS arrives in May)
 * 28 - Lizzie Lewis is murdered by Ed Morgan. (TW: Ghost Machine)
 * Late March - The TARDIS materializes in the junkyard at 76 Totter's Lane, owned by I.M. Foreman, in the Shoreditch area of London, its 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 unusual cold wave.

April

 * 1 - The events of Time and Relative take place

October

 * Late October - The Doctor has made arrangements with a local funeral parlor to bury the Hand of Omega in a nearby churchyard. (DW: Remembrance of the Daleks)
 * Concerned about the unusual behaviour of one of her students, Susan Foreman, schoolteacher Barbara Wright attempts to investigate by, among other things, visiting the address given as Susan's - only to discover that it's a junkyard. She eventually builds up the courage to ask a fellow teacher, Ian Chesterton for advice. (DW: ''An Unearthly Child)
 * Barbara Wright and Ian Chesterton follow Susan Foreman to a junkyard at 76 Totter's Lane. Further investigation leads to a tense encounter with a mysterious old man attempting to enter a police box. Forcing their way inside the box, they discover a strange vessel capable of travelling in time and space. The old man, fearful that the two schoolteachers might change history by revealing what they have seen, kidnaps them by activating the vessel, the TARDIS, which whisks the group away to prehistoric Earth. (DW: An Unearthly Child)

November

 * Sometime before the 22nd - The Spacefleet fighter Tisiphone, which had fallen into a temporal rift in 2547 during a battle with Daleks, exits the temporal rift near Earth space. Its crew manages to escape to England. (NA:Return of the Living Dad)
 * 22 - In Texas, 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. (MA: Who Killed Kennedy) The Ninth Doctor is in the crowd watching President Kennedy's motorcade drive by just before the President is assassinated. A photograph which shows the Doctor among the spectators later finds its way into Clive Finch's collection of files about the Doctor. (DW: Rose) As far as the general public is concerned, the man responsible for the killing is Lee Harvey Oswald, although conspiracy theories about the actual culprit persist for decades afterwards.
 * 23 - The Doctor and Ace arrive in London, with the Doctor returning to the site of 76 Totters Lane and Coal Hill School intending to complete some unfinished business involving the Hand of Omega, which had been interrupted by an abrupt departure centuries earlier (subjective time) (DW: Remembrance of the Daleks and An Unearthly Child). The Daleks, led by Davros, attempt an invasion at this time, leading to a major gunbattle at Totters Lane. Meanwhile, a new science-fiction serial, Doctor ___, begins broadcasting on the BBC. (DW: Remembrance of the Daleks) The Nemesis passes by Earth, heralding the assassination of President John F. Kennedy (see below). (DW: Silver Nemesis)
 * 24 - Elsewhere on earth, Lee Harvey Oswald, the man accused of assassinating John F. Kennedy, is himself assassinated in Dallas by Jack Ruby.

Unknown date
Nyssa is born on Traken.

In John Smith's fictional future, he dies in this year (DW: The Family of Blood)

April

 * 27 - Russell T Davies, Head writer and executive producer of Doctor Who from 2005-2009 and writer of Damaged Goods is born in Swansea, Wales.

September

 * 19 - First filming session for the show. A one day shoot at Ealing

October

 * 09 - Filming resumes at Ealing for An Unearthly Child
 * 11 - Filming ends at Ealing for An Unearthly Child
 * 11 - One day studio filming at Lime Grove Studio D for An Unearthly Child
 * 25 - One day studio filming at Lime Grove Studio D for An Unearthly Child. Margot Maxine, an extra hired as a member of the tribe, walks out at 3:00 after refusing to have her teeth blackened

November

 * 01 - One day studio filming at Lime Grove Studio D for An Unearthly Child
 * 08 - One day studio filming at Lime Grove Studio D for An Unearthly Child
 * 22 - Filming of an episode of The Daleks is interrupted by the news of US President John F. Kennedy's assassination earlier that day.
 * 23 - Doctor Who debuts on UK television with the first broadcast of An Unearthly Child. Some parts of the UK are unable to view the episode due to a power cut.
 * 24 - Real-life events continue to overshadow fiction as Lee Harvey Oswald, accussed assassin of John F. Kennedy, is himself gunned down on live television.
 * 30 - "An Unearthly Child" Broadcast for second time as many viewers missed the original screening as a result of a power cut. The rebroadcast is followed by the first broadcast of "The Cave of Skulls" (An Unearthly Child Episode 2)

December

 * 07 - "The Forest of Fear" First Broadcast (An Unearthly Child Episode 3)
 * 14 - "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)

Unknown Date
Julian Bleach, who plays the Ghostmaker in Torchwood and Davros in Doctor Who is born in Bournemouth.

Reference

 * A History of the Universe by Lance Parkin