Ewan
I was born in Cambridgeshire in 1954. I have always known the "Chase me Charlie" variant, my mother having sung it to me since I was tiny. I have asked her and she believes that she has known it since she was small (the 1920s) and that her mother (born 1905) knew it to sing to her.
My mother believes that she knows the "Auntie Mary" version but cannot say if she always did. She certainly never sang it to me and it seems quite likely that I taught it to her after having heard it in the north of England. My North Yorkshire in-laws know this version, again into the previous generation which means that it is probably pre-war.
There is some other evidence about "Chase me Charlie". Denis Murphy, the famous Irish fiddler, lived in London for quite some time before returning to his native Kerry. He took back with him a number of tunes which appear to have previously unknown in Kerry. These included "Denis Murphy's Slide" (in fact a straightforward version of "The mucking of Geordie's Byre") and the ubiquitous "Cock of The North" which he called "Chase me Charlie".
By the way, I don't agree with a previous contributor to a previous thread that anything with "Charlie" in it is to do with a claimant to the Scottish throne. This seems to be a good example of one that isn't.
Cheers!!! Ian