Eadred, King of the English 923-955, was titled Regis qui regimina regnorum Angulsaxna, Norþhymbra, Paganorum, Brettonumque ("Reigning over the governments of the kingdoms of the Anglo-Saxons, Northumbrians, Pagans, and British").
His successor, Eadwig the Fair, 955-959 was titled Rex nutu Dei Angulsæxna et Northanhumbrorum imperator paganorum gubernator Breotonumque propugnator ("King by the will of God, Emperor of the Anglo-Saxons and Northumbrians, governor of the pagans, commander of the British").
Why did they feel the need to list the Anglo-Saxons and Northumbrians separately? Were the Northumbrians not considered to be an Anglo-Saxon group?
I am in no way a historian and this is my first time trying to answer a question so bare with me. During the middle ages countries were a lot more subdivided than they are today. For instance, in England specifically you had Northumbria, Mercia, East Anglia, and Wessex. All of these regions had different rulers up until they were united by Athelstan in the 10th century due to the looming threat of another viking invasion. It should be noted that prior to the 9th century there was unification within England of the 7 states of the Heptarchy. However, when the vikings came in they disturbed this unification and once again the states split. Focusing in more on your question, from what I've found, Northumbrians were part of the Anglo-Saxon group we refer to today, unlike the Welsh and Scots. However, the vikings took over Northumbria in 866 after a full scale invasion. In 944 the king of Wessex, Edmund, would take back Northumbria and drive out the Danes. To make the connection as to why Edmund is not referenced and Eadred is, Eadred was Edmund's son. Northumbria was passed down to him in 946. Presumably since the kingdom was separated from the rest of Anglo-Saxon England for 80 years, when the Anglo-Saxons regained the territory they felt the need to address them differently. There was also a change in the way the areas were run. A fair amount of Danes stayed in Northumbria, thereby making it not strictly Anglo-Saxon anymore. I think a large amount of the reasoning for referring to the Northumbrians separately can be attributed to the Danes.
These sites provide a more in depth background: http://www.englandsnortheast.co.uk/KingdomofNorthumbria.html http://historymedren.about.com/od/hterms/g/Heptarchy.htm http://www.englandsnortheast.co.uk/VikingNorthumbria.html
Another source I used is unfortunately probably not easily available to you, but a lecture from Professor Charity Urbanski at the University of Washington.