i) births and deaths
Nothing that caught my eye for this date.
ii) webcast anniversary
13 July 2001: release of the pilot webcast episode of Death Comes To Time, the weirdly canon-violating and very long Seventh Doctor story, basically an audio with animation.
iii) dates specified in canon
13 July 1643: the battle of Little Hodcombe, and surrounding time-travel events involving the Fifth Doctor, as shown in The Awakening (1984).
13 July 1964: the events of the earlier phase of Whatever Happened To Sarah Jane? - was it Andrea or Sarah who drowned? The best of the first series of SJA for my money.
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