11 June 1927: birth of Kit Pedler, who co-wrote The Tenth Planet (First Doctor, 1966), The Moonbase (Second Doctor, 1967) and The Tomb of the Cybermen (Fourth Doctor, 1967)
11 June 1931: birth of Colin Bell, who played Chief Petty Officer Summers in The Sea Devils (Third Doctor, 1972) and Private Bryson in Invasion of the Dinosaurs (Third Doctor, 1974).
i) broadcast anniversaries
11 June 1966: broadcast of third episode of The Savages. Jano has absorbed the Doctor's essence and starts to behave like him.
11 June 2005: broadcast of Bad Wolf. The Doctor, Rose and Jack find themselves participating in TV game shows, but the Daleks are behind it all.
ii) date specified in canon
11 June 1925: events of Black Orchid (1982).