C-Day was set for Monday 16 July 1966, but was cancelled when WOTAN was destroyed following its failed attempt to take over London with its War Machines. (TV: The War Machines, PROSE: Who Killed Kennedy)
On 16 July 1969, the Saturn V rocket that held the Apollo 11 pod on its mission to the Moon was launched from the Kennedy Space Center. The Tenth Doctor watched this launch from the ground. Meanwhile, after Apollo had picked up a visual of unidentifed objects, the secret agents, Spencer and Milledge, took command of Mission Control. (PROSE: Blue Moon)
Behind the scenes
This was one of very few instances in which an old series Doctor Who television story, namely episode four of The War Machines, took place on the same day as its broadcast: 16 July 1966. Another such example is 28 February 1981. The new series had three such occurrences: 25 December 2009, 26 June 2010 and 25 December 2009.
Within that same serial, though, the 16th of July is portrayed as a Monday, when in the real world 16 July 1966 was a Saturday.