Northumbria

Hmmm, well your time limits sort of straddle two different eras in England--the Anglo-Saxon/Danish era and the Norman era.  So, I'd say that Northumbria was throughout Anglo-Saxon times sort of a seperate, dinstinct region that evolved into a cultural, religious, and intellectual center.  I'd nearly go as far as to say that when most people think of Anglo-Saxon England, they envison Bede.  Of course others might think of the South Saxons (Sussex) or the West Saxons (Wessex) whose political contributions were paramount in the development of a consolidated England, which I fear can't be seen realistically until after William the Bastard consolidated his new kingdom with the Doomsday report.  Administratively England didn't exist except on paper until 1066--in my mind at least.  To go back to your question, Northumbria became much more integrated follwing the Norman invasion and became the Norman-English frontier bordering Scotland.       

As with the Welsh Marches, the Normans increasingly began to control Northumbria politcally.  Of course the Scots and Welsh didn't always cooperate with the Normans.  Through time Norman families infiltrated the old Scotish regimes.  My mother's family name--Gordon is a large clan known to be a mix of Scot and Norman.  Any of the nobles of the period in Scotland and England attempted to secure their lineages by marrying their offspring off to Norman aristocrats.  Nonetheless, the Scots continued, as I'm sure you all know to disrupt and disagree over territorial boundaries for centuries, until finally they won the crown with the coronation of the Stewarts--another of my maternal family names...