Could be Patrick Troughton's Doctor, or Lorna Watson's Sister Boniface, or possibly Sister Boniface making a TV reference to Doctor Who. After a bit of research, the last one is unlikely. Patrick Troughton became the Doctor in 1966. Sister Boniface takes place in the early sixties. I mention this only because IMDB has a Trivia item about her referencing the second Doctor in the episode that is a Doctor Who inspired. S3, E3, Professor Y. It may be the writer of Sister Boniface paying tribute to the Doctor, but Sister Boniface uses the phrase a year earlier in S2, E3, The It Girl. Both episodes were written by Neil Irvine. I'm now wondering how many other episodes she says it in. Is it a Sister thing, or is it a Neil Irvine thing?
The phrase is a common expression that goes through cycles of popularity. One source I found said it first appear in print in The Journal of a Disappointed Man, 1919, by W. N. P. Barbellion. I read another reference that said it was used in replacement of Oh My God. So it seems reasonable that Sister B. would use Oh My Giddy Aunt as a substitute.
So -
TV reference to the second Doctor?
TV reference to Sister Boniface?
TV reference of the Sister Boniface writers making a TV reference to Doctor Who.
I haven't said it lately, but I'm just pulling all this out of thin Ethernet air. I'm am not an authority about anything.