7 July 1919: birth of Jon Pertwee, the Third Doctor, star of the show from 1970 to 1974; the first Doctor I can remember, the gentleman wizard who spends a lot of his time on Earth.
7 July 1948: birth of Mat Irvine, responsible for many of the special effects on the show in the late 1970s. He wrote a book about it.
7 July 1985: death of Ewen Solon, who played Chal in The Savages (First Doctor, 1966) and Vishinsky in Planet of Evil (Fourth Doctor, 1975).
7 July 1997: death of Royston Tickner, who played Steinberger P. Green in "The Feast of Steven", the seventh episode of what we now call The Daleks' Master Plan (First Doctor, 1965) and Robbins in The Sea Devils (Third Doctor, 1972).
7 July 2019: death of Stacy Davies, who played Perkins in The Invasion (Second Doctor, 1968) and Veros in State of Decay (Fourth Doctor, 1980)
ii) broadcast anniversary
7 July 2009: broadcast of the second episode of Torchwood: Children of Earth, with Jack reassembling his exploded body, getting encased in concrete and then busted out by Ianto, while Gwen and Rhys head for London and the children chant, "We are coming tomorrow." Here's senior civil servant Frobisher trying to get a grip on the situation. (Apparently the actor playing him also appeared in Doctor Who a couple of times.)
iii) date specified in-universe
The short story "Salva Mea", by Joe Lidster, in the anthology Short Trips: Snapshots, featuring the Eighth Doctor with Charley Pollard and C'Rizz, is set on 7 July 2007.