Couldn't find any.
ii) broadcast anniversaries
4 July 1964: non-broadcast of 'Hidden Danger', the fourth episode of the story we now know as The Sensorites, because of the gripping events at the third test match of the 1964 Ashes series (idf you're interested, Australia took five wickets in the course of the day, and another five when the second innings resumed on Sunday; England were unable to make up the difference and so lost the Ashes as per usual), also the Wimbledon women's final between Maria Bueno and Margaret Smith (later Margaret Court) which Bueno won 6–4 7–9 6–3 (Smith having defeated 19-year-old Billie-Jean Moffitt, later Billie-Jean King, int he semi-final - revenge for their match two years earlier having gone the other way when Smith was the world's #1 seed). Aren't you glad I told you that?
4 July 2008: release of The Baktek Illusion, tenth and last of the Doctor Who Writers' Comics.
I admit I'm really scraping the barrel here. 4 July is a significant anniversary in some well-known real-life historical contexts, but not really for Doctor Who.