1 May 1946: birth of Joanna Lumley, who played the Thirteenth Doctor in The Curse of Fatal Death (1999).
1 May 1984: birth of Sacha Dhawan, who played Waris Hussein in An Adventure in Space and Time (docudrama, 2013) and the Master in 2020.
1 May 1985: death of George Pravda, who played Denes in The Enemy of the World (Second Doctor, 1967-68), Jaeger in The Mutants (Third Doctor, 1972) and Castellan Spandrell in The Deadly Assassin (Fourth Doctor, 1976).
1 May 2002: death of John Nathan Turner, producer of Old Who from 1980 to 1989 (and of Dimensions in Time in 1993); controversial and colourful, like him or loathe him, nobody can dispute the depth of his influence on the show.
1 May 2008: death of Bernard Archard, who played Bragen in The Power of the Daleks (Second Doctor, 1966) and Marcus Scarman in The Pyramids of Mars (Fourth Doctor, 1975).
ii) broadcast and production anniversaries
1 May 1965: broadcast of "Dimensions of Time", second episode of the story we now call The Space Museum. Lobos, leader of the Moroks, starts to hunt down the Tardis crew.
1 May 1971: broadcast of fourth episode of Colony in Space. The Doctor and Jo confront first the Guardian of the primitives and then the Adjudicator, who turns out to be the Master.
1 May 1974: Jon Pertwee and Tom Baker film the Third to Fourth Doctor regeneration sequence. Frankly the broadcast version was a bit disappointing; here's one of many fannish improvements.
1 May 2010: broadcast of Flesh and Stone. The clerics start to disappear, but the Doctor manages to tumble the aliens into the mysterious crack, and then has a narrow escape from Amy.
iii) dates specified in-universe
1 May some time in the 1970s: setting of the last scenes of The Dæmons (Third Doctor, 1971).
1 May 1643 and 1984: setting of The Awakening (Fifth Doctor, 1984).