This is a matter of great ongoing debate. The great Northumbrian chronicler and 'father of English history', Bede, discusses the idea of a gens Anglorum as early as the eighth century, which to his mind also includes the gens Saxonum to the south. Until the late Anglo-Saxon period, the centres of power within the multiple kingdoms of 'England' changes relatively often. At the time of the Augustinian mission in 597, the centre of power was in Kent, followed by East Anglia. By the time of Bede's writing, the dominant kingdom in Anglo-Saxon England was Bede's native Northumbria, which was also largely ethnically Anglian. Its main rival and eventual successor was Mercia, another predominantly Anglian kingdom, referred to only ever as the Anglii in the Welsh chronicles of the Annales Cambriae. To Bede, therefore, it would have seemed perhaps only natural that a unified England would have been largely Anglian in culture and politics, since the leading Saxon kingdoms, Essex and Sussex, were client states of the Anglian kingdoms, and Wessex was a relative backwater. Although the political landscape of England changes tremendously in the late eighth and early ninth centuries, Bede retains his position as major influence on English writing and political thought, and so the idea of a gens Anglorum sticks, even in nascent Saxon polities.

Pauline Stafford also suggests that there is a distinctly propagandistic element to the adoption of the title of Rex Anglorum by English kings. Although the unified Kingdom of England inherited by Æthelstan in 924 is primarily West Saxon in nature, it rests heavily on the Anglian kingdom of Mercia, which had been ruled by his aunt Æthelflæd, for support. It also extended a very fragile political control over the Anglo-Scandinavian regions of the Danelaw and the former kingdoms of Northumbria, to which the West Saxons were as much an invader as the Danes had been. Indeed, it's not until the reign of Edgar in the 970s that the North is finally fully pacified.

Æthelflæd, herself a Saxon, had ruled Anglian Mercia through careful and clever politics, patronising Mercian and Anglian saints and culture, appealing to local customs and traditions and fostering close relationships with her nobility. According to William of Malmesbury, Æthelstan spends much of his childhood at Æthelflæd's court, learning the importance of clever politicing and good propaganda to maintaining a stable rule. In fact, the Anglo-Saxon Chronicle records that Æthelstan is first elected as king among the Mercians before he becomes King of All England after the death of his father and brother in short succession. Following a victory over the Anglo-Scandinavians, Danes, Scots and Irish at Brunanburh, Æthelstan actually declares himself Rex totius Britanniæ or King of all Britain, although on coins from Derby, he's still called Rex Saxonum. The adoption of the gens Anglorum may therefore have been a political sop to the people of Mercia, East Anglia and Northumbria that although the new kingdom originated from a West Saxon expansion, the Angles would still have a political voice and an equal share in the kingdom that they had helped to build.

Some reading:

Wormald (1994): Engla Lond: The Making of an Allegiance

Stafford (2008): 'The Annals of Aethelflaed - Annals, History and Politics in Early Tenth Century England'

Molyneaux (2016), The Formation of the English Kingdom in the Tenth Century