The "Little Pet Polka" recorded by James Brown in 1911 is NOT the same "Little Pet Polka" by Louis Wallis. It is, however, the same tune as "The Blue Bell Polka".

There is also a book called "Song Dance and Merriment" published by Mozart Allan (Glasgow, n.d.) which includes "The Little Pet Polka" with no attribution. The arrangement is slightly different:

       The "A" part is identical to the A part of Blue Bell; the B part is what we know as the Trio
       (the third part or C part) in Blue Bell, but rendered in D major instead of the usual
       C major; the C part is what we know as the B part of Blue Bell, but rendered in C major
       instead of D major. Whew!

F Stanley remains a mystery; I have seen references to the composer being one Florence Stanley, but haven't chased it up to any conclusion. It's fairly obvious that it was not composed by the Irish accordionist Fintan Stanley, despite many internet claims that it was.