WITH MY LITTLE STICK OF BLACKPOOL ROCK has been posted a couple of times at Mudcat. See the threads called:

Lyr/Chords Req: With ... Blackpool Rock (G Formby)

Lyr Req: Blackpool Rock--She likes a little bit.. -- although here, it wasn't the song that was asked for.

Like a lot of Formby's songs, WITH MY LITTLE STICK OF BLACKPOOL ROCK was written by Frederick* Cliffe, George Formby, and Harry Gifford.

*Funny thing, though, several web sites—a minority—spell his name Federick Cliffe, not Frederick.