It turns up as number 5391 in the Roud Folk Song Index. Only one example is listed so far: a set recorded by Mike Yates from George Fradley of Sudbury, Derbyshire, in 1984. It appears on the cassette tape One of the Best (Veteran VT 114): Veteran website.

The following is quoted from Mike Yates, The Other Songs, published at the Musical Traditions website:

"The splendid Derbyshire singer George Fradley was also heavily indebted to the Music Hall recordings. In his youth George had performed in a family troupe that toured the local villages and many of their songs clearly came from the Music Hall. His lovely comic song Mary Ann, She's After Me was recorded twice by George Bastow, firstly in 1911 (Columbia 1869) and then two years later, in 1913 (John Bull H-32)."

The song also seems to have been recorded by Albert Whelan, "The Australian Entertainer", who became successful in the music hall in Britain from the very early years of the 29th century, later moving into broadcasting and films (Yiddle on your Fiddle / Mary Ann She's after me Valk343). It appears from info in another thread here that he recorded Yiddle on the Fiddle in 1912.

Unfortunately, the person who posted in the thread Sorcha mentions failed to quote writer credits from the tape concerned. A lead of that kind would have been helpful.