Update: I was able to find a picture of the 45 rpm record I bought. The song writing credit went to:   Traditional - Arr by H. Pye

As to the Jimmy Drew recording above, the songwriter’s credit was given to Jimmy Drew, however you need to realize an old trick of the publishing/recording industry was to simply take writing credit for public domain songs just to get a royalty.

That is also what the Arranger credit was for.

As to who H. Pye was, maybe it was a drummer or just a pseudonym for someone who knew they could make a buck off the credit.