Are you sure about that?
Could be she was a few marbles short- or had a few too many. Examples show that there are several meanings, but...
It seems that the 'in lieu of God thing' is the meaning most found currently in UK.

Oh, my aching back, there are still other possibilities to those I posted.
One is that it dates from the time of the play, "Charley's Aunt," thus (perhaps) meaning impetuous. (dubious)
Another, from Australia- Giddy aunts are keepers of family stories and tales. Another usage there- keep a giddy store (one with all sorts of things, old and new, for impulse buyers and collectors.
"Oh my Giddy Aunt" is a musical comedy by Moran and Kayden.

One used by Americans, no relation- I knew right from the giddyap about that .... See Lighter, Historical Dictionary of American Slang.
Lighter does not include the expression current in England.