"Oh, my giddy aunt" was a colloquialism that was often used as an exclamation of surprise.
The Brigadier said this when he found out that Professor Rubeish was missing. (TV: The Time Warrior)
The Second Doctor used the phrase often. He said it to Dastari during an argument in the cellar (TV: The Two Doctors) and said it when surprised by a Kroton. (TV: The Krotons).
He also said it to Sgt Benton as a Gell guard tried to enter the TARDIS. (TV: The Three Doctors)
Mrs. Wibbsey exclaimed it to Buddy Hudson and a cultist when realizing something was wrong with the Fourth Doctor (AUDIO: Starfall)
A clone of the Second Doctor said it as Lucius threatened to devour him. (AUDIO: Survivors in Space)
Missy said it to Osgood while they were on a plane. (TV: Death in Heaven)