Northumberland is, politically, part of England; no special pleading is going to change that. Your argument can equally be applied to all the regions that comprise England; and, for that matter, to the regions of most (if not all) countries in the world. Is Aberdeenshire Scottish? Is Kerry Irish? Is the Ardèche French?

Where traditional vernacular cultures are concerned, the regional/local approach is generally more productive when attempting analysis; 'national' culture is largely an artificial construct. To deny that the regions of a country are part of that country is unhelpful, however, and will inevitably weaken any argument which includes that assumption.