Prior to the formation of The Scott Owners’ Club in 1958, there were several Scott clubs, the largest of which was, I believe, in the Sheffield area, but this was The Sheffield Scott Club. I don’t really know the history of earlier clubs, and perhaps if you could put a photo of the badge onto this website, somebody may recognize it and say where and when it is from. The ACU might also have a record of it.
I wrote an article for Yowl October 2009, which included a picture of a selection of Scott club badges on page 205, and was to answer a question from another NW member whose Scott was fitted with a club badge from new. Let me know if that helps you identify your badge.