16 July 1964 was that day that the last episode of The War Machines, which was also the last episode of the original third season, was broadcast. The Doctor invents a way of neutralising the War Machines, defeats WOTAN, learns that Dodo is staying in England, and takes off with new companions Ben and Polly unintentionally on board.
16 July is also specified in the script of The War Machines as "C-Day", the day when all the computers in the world are to be linked (and then WOTAN will rule supreme). The problem is, Sir Charles Summers specifies very clearly in Episode 1 that C-Day will be on Monday 16 July; and 16 July 1966 was, obviously since Doctor Who was on telly that evening, a Saturday - the next Monday 16 July was in 1973 (and the previous one, in 1962, is impossible because the Post Office Tower had not yet been built). For reasons we shall explore next Tuesday, this creates other problems. I prefer to think that Sir Charles misspoke and meant Saturday, or the 18th, and the journalists at the press conference were too polite to correct him. This would make them rather unusual journalists, but Doctor Who is a show about unusual people.