I have three works (books) of my own that have touched on the geographic boundary of Northumbria. Here's my two pennyworth:
Since the rise in fortunes of Newcastle United (the Keegan era) there has been a corresponding profile given to things Geordie, even attempts to define the term geographically. This has smacked to me from parochialism at best to simply an attempt to exclude the Mackems from the feast. During the run of the highly successful What Cheeor Geordie radio show in the 50s & 60s the term Geordie included Tynesiders, Wearsiders and Durhamites for sure (witness the words to 'Wherever you go you're sure to find a Geordie'). Even now some believe the term Northumbrian means Northumberlanders and excludes the rest. More lenient folks in the North East will accept Tweed to Tees, but for some of my work it suits my purpose to include Tweed to Humber. For my culinary project I have even expanded it to its full historic expanse from Edinburgh south to Hull.
As far as music goes, well. Prior to the industrial revolution I can only guess -- there must have been monastic and other church music of course as it was a centre of Christianity. We don't know for sure the Northumbrian pipes did or did not exist, only that there seems to be no mention of them until relatively recently. Fertile ground for the military, who were musical among the ranks and like all British troops well-travelled. Long established fishing industry and its traditions. I think in those days it must have been very like any other part of Britain with music outside of church confined to fairs and travelling minstrels.
With the Industrial Revolution the incomers must have brought along new traditions: Cornish, Irish, Scots, Welsh et al so that the region became very cosmopolitan. I think the 'Geordie' was born of this era.
It may be heresy, but I don't believe there is a Northumbrian music, just music made Northumbrian by its content and rendition.
And yes, Brian Johnson's Byker Hill is now part of my own repartoire -- I believe modern rendition is essential to keeping the folk music alive. I think without Lindisfarne, Katheryn Tickell, Sting, Mark Knopfler, the Hush, etc. producing 'new' Northunmbrian music over the last three decades, we'd be looking back at those lovelty songs from Brannigan's generation as a dead genre.