It looks like you are right - they are a pan-baked scone from Northumberland (top right hand corner of England, just before you bump into the Scottish border country).

http://www.hwatson.force9.co.uk/cookbook/recipes/baking/singinhinnies.htm

As you said the story takes place in Scotland or England, here's why it was probably a bit of both - the area changed sides so often I think people were never quite sure if they were English or Scottish:
http://www.hwatson.force9.co.uk/regional cooking/northumbria.htm

And here's a song to finish:
http://www.geordietheme.tyneside.com/billy.html