Saw Gideon's Way 1.3 The Firebug when a Police Box turned up at 45.07:
www.youtube.com/watch?v=c7tiL2eyrfcThe Firebug came on November 28 1964 which was on the same evening of the second episode of The Dalek Invasion of Earth, The Daleks.
However somewhat ironically the TARDIS was nowhere to be seen in The Daleks especially since Doctor Who and Gideon's Way were each on rival networks - Doctor Who on the BBC and Gideon's Way on ITV.
Perhaps Doctor Who had lent its Police Box to Gideon's Way on that very night!
Incidentally in Gideon's Way, Malcolm Gideon, the younger son of the title character was played by Giles Watling, Debbie's younger brother.