Watson, I did say "suspect," and for a good reason. Bill himself sold me the song-sheet at a gig of his in Coventry. I don't know who printed it. About 1973. Good Grief.
There isn't a Bow Bells for Brummigem. Halfway down the road from Coventry will do. Dont take it too seriously.
There isn't a Brummigem either. Long ago, in a serious attempt to find the origin, I laboriously went through the Doomsday Book looking for it. No Birmingham, but there was a Brymwichham. Sounds near enough folk memory for me. Regards.