Not too sure of the exact location, but Byker is either a suburb, or near to, Newcastle on Tyne. Newcastle was once, before local government reorganization, the county town of Northumberland in the the North east of England, in fact the Northern border of Northumberland is the Scottish border.

At one time one of the biggest coal mining areas in Europe, hence the saying "taking coals to Newcastle" meaning doing something totally pointless.

Cannot verify for certain where they were, because they would almost certainly be closed now, but Byker Hill and Walker shore are certanly the names of coal pits. The latter name may be a reference to a pit that extended under the North sea, as do quite a lot of the coal measures in that area.

I have not looked it up in the DT, but I assume Byker Hill is traditional, the only recording I have (by the Barely Works), claims it as such. I have heard it sung by quite a few people, around Manchester and elsewhere in the UK, and never heard anyone identify a writer.

If you are interested, there are loads of references to coal mining in the North East of England in Jez Lowe's songs, although he is from the next county south of Northumberland, County Durham. Small coals (about the hardship of mining in narrow seams) and Gallaways ( about the fate of the pit ponies when the mines were closed) spring to mind. There are of course many levels of interpretation to Jez's songs, these are very glib descriptions.

Hope you find this helpful