It looks like an extract from Seed's Wigan & District Directory for 1925/6. There's a copy (for reference) in Ashton library - top shelf, third bay along from the Sure Start desk if memory serves...

Town: Ashton

Thanks for posting that directory list Dougie. I've seen it before, and it contains a lot of familiar names, including my great grandad John Ashton at 241.
The Drum would be on the even-numbered side of the street, and maybe it wasn't listed because nobody actually lived there? I believe it was in existence at that time, or soon after, although in an earlier building.
I've asked everybody I can think of and not come up with a convincing answer to how it came to be called the Drum.