The idea of a unified Anglalond had been knocking around since at least the 7th Century, when it's first postulated by Bede. Interestingly, it's also about this time that we start to see a more concrete use of "ethno-nationalist" identifiers by English kingdoms, e.g. The Northumbrians are Anglian. There isn't one solid "identity" in Early Medieval England; the Seventh and Eighth Century Kings of Kent identified themselves not with any English or Jutish identity, but with the Cantwara, the Brythonic regional identity, while pan-Mercian identity appears to have been political rather than ethnographic. Mercian rulers typically identify as Merciorum rather than Anglorum, although this is likely due to the hegemonic/federated nature of Mercia.

Actually, how the English chose to identify is rather academic to the question. Certainly, by 1066, England had been a unified country for well over a century. The idea that English history "starts" in 1066 is rather a relic of Victorian approaches to history. Beginning largely with F.W. Maitland's The Anglo-Saxons, the 19th Century saw a burgeoning of interest in the study of Early Medieval England, although unfortunately this was largely carried out in a way that can charitably be called haphazard. Anglo-Saxon Studies (indeed even the term Anglo-Saxon itself) arose from a culmination of Whig history and an academic imperative to justify at all costs the actions and influence of the British Empire. This is the approach that birthed ideas like the witan being a proto-democratic Parliament in order to call England "the mother of democracy" and justify the "civilising mission" of Empire. Alfred's embrace of learning and English translation, as well as his military reforms, were construed as an implicit foundation for the Anglican church and the importance of missionary work in a colonial context.

While in many ways there was a lot of continuity in 1066, there was also significant change, in particular legal upheaval and vast changes in land tenure, and significant changes within the Church. Through the wonky lens of the 19th Century, 1066 marked The Great Event when freeborn, democratic Englishmen were subjected to the yoke of foreign oppression, the year in which everything changed, and the year from whence the English were striving to reclaim those earlier rights and freedoms. Sellar and Yeatman's excellent parody of 1930s and earlier English history teaching, 1066 and All That nails the prevailing academic tendency of the time:

In 1066 occurred the other memorable date in English History, viz. William the Conqueror... who decided everybody had to belong to somebody else and everybody else to the king.

With a historical educational approach that was more concerned with the rote learning of names and dates rather than any genuinely nuanced approach, it's not surprising that 1066 has entered the pop-cultural consciousness as the year in which English history "began".

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In order to answer this question I believe it to be important that we fully examine four important periods of history in Anglo Saxon England: later Anglo-Saxon Kingdoms, Alfred the Great, Athelstan and Alfred's Descendants and Alfred's Legacy in the ideas of Nationalism.

The Later Anglo Saxon Kingdoms: While East Anglia, Wessex, Mercia and Northumbria would all be considered later Anglo Saxon kingdoms, here I will focus primarily on Mercia and Northumbria, and the rise and fall of each.

• Northumbria: Northumbria was a country of constituted of two main regions, Bernicia and Deira. A king of Bernicia, Ida's grandson Aelfrith, was the first ruler to unite the two polities under his rule. He exiled the Deiran Edwin to the court of King Rædwald of the East Angles in order to claim both kingdoms, but Edwin returned in approximately 616 to conquer Northumbria with Rædwald's aid. Edwin, who ruled from approximately 616 to 633, was one of the last kings of the Deiran line to reign over all of Northumbria; it was Oswald of Bernicia(c. 634–642) who finally succeeded in making the merger more permanent. The final unification of these two distinct lands allowed Northumbria briefly to flourish, if only for a short time. As evidence for this I might point to the churches at both York and the church of Hexam buily under Wildred and Benedict Biscop (which according to Biscop's biographer no church south of the Alps could rival). These churches were designed by stonemasons brought from Gaul and made in the styles of the Mediterranean, evidence of Northumbria's cosmopolitan presence. The eventual decline of Northumbria was almost entirely due to the continual threats it faced from both the Scots and the Danes, and as the 8th century drew to a close, Northumbria's supremacy waned even more.
• Mercia: Mercia rose to power around a similar time as Northumbria, brought to glory under King Penda (633-655), who both crippled the newly formed Northumbria and briefly brought power over even the southern kings. While this expansion was temporary (and Mercia would not yet grow to its territorial height until nearly a century later), this did establish Mercia as a powerhouse in the region. Over the next century the ebb and flow of rulers in the surrounding kingdoms allowed Mercia to expand both north and south (map linked: https://en.wikipedia.org/wiki/Mercia#/media/File:Mercian_Supremacy_x_4.svg )
• Conclusion (why am I mentioning these?): Both Mercia and Northumbria experienced great victories and territorial growth during the centuries preceding Alfred. Their feats might even be considered greater than his in Wessex, but they might not have been as chronicled or reknown in modern tellings of the history of England, this literary bias is important to keep in mind as we examine the life of Alfred.

Alfred the Great, the First to Dream of an England: Simon Keynes might summarize the popular legend of Alfred best:

King Alfred the Great has long been regarded as the archetypal symbol of the nation's perception of itself. Beset throughout his reign with the reality or threat of Viking invasions, Alfred batded fiercely and suffered heroically in leading his people to their eventual victory; at the same time he promoted the causes of religion and learning, and by the example of his government upheld truth, justice and the Anglo-Saxon way. Moreover, although himself fundamentally English (with West Saxon parents and a Mercian wife), he stood for a combination of political interests which made it easier to pass him off as prototypically British.

Alfred the Great (849-899) was a king of Wessex who defended the kingdom through multiple Danish raids, established new laws of governance and assured that his legacy would not be lost through planting both his son and daughter in prominent positions following his death. He is also often regarded as the first to have a vision of a singularly united Christian kingdom of England. Whether this is truly accurate or exaggeration I will discuss later, but it is nevertheless crucial to note as Alfred might be the most important figure in the idea of a unified England (or English heritage).

Alfred's Successors:

• Aethelflaed of Mercia: While many consider Edward (son of Alfred) to be one of the most important successors of Alfred, I instead intend to dive into his daughter Aethlflaed of Mercia (870-918). Aethlflaed was married young to an ealdorman of Mercia, Aethlred. Following his death however, she rules as a Queen of Mercia beside her brother Edward. The ruling of the two siblings is in my mind the final unity of two of the most powerful kingdoms. Rather than the two kingdoms being united through marriage alone, the establishment of two siblings on the thrones allowed for both to act in conjunction and for Wessex to eventually dominate Mercia.
• Æthelstan: While Æthelstan is often overshadowed by his grandfather, his achievements are tantamount if not greater than Alfred's. Æthelstan centralised government; he increased control over the production of charters and summoned leading figures from distant areas to his councils. These meetings were also attended by rulers from outside his territory, especially Welsh kings, who thus acknowledged his overlordship. More legal texts survive from his reign than from any other 10th-century English king. They show his concern about widespread robberies, and the threat they posed to social order. His legal reforms built on those of his grandfather, Alfred the Great. Æthelstan was one of the most pious West Saxon kings, and was known for collecting relics and founding churches. His household was the centre of English learning during his reign, and it laid the foundation for the Benedictine monastic reform later in the century. No other West Saxon king played as important a role in European politics as Æthelstan, and he arranged the marriages of several of his sisters to continental rulers.

All of these factors may seem tangential to your question regarding the idea of England, but I promise they are important. What all of this evidence reveals is that the idea of a common England might not be as concrete as you may think. What the rise of Mercia and Northumbria reveal is that Wessex's ascension, while important, was likely not as unprecedented as it is made out to be. While Alfred and his successors created a united kingdom, the importance of them might be exaggerated (I'd reference the map of Mercia at it's territorial height where it encompassed nearly all of modern day England. The legacy and history of Alfred are complicated, and popular culture may lead one to believe in an idea of a powerful and unified force of common peoples, that began with the vision of Alfred, eventually fell in defeat to the Normans, the Danes and Northmen against they had fought for so long. But these romanticized ideals are likely a skewed vision of the reality of England. The texts of the 13th, 14th and 15th centuries actually do not refer to Alfred as "the Great" rather this term, and his romanticization actually only appear in the 18th century. Simon Keynes explains this phenomenon

Henceforth Alfred could serve as a paragon of enlightened and, 'constitutional' kingship, as the originator and personification of the most chershed institutions of government, as the protector of liberty and order, as their defender of his people from foreign powers, as the guardian of their religious beliefs, and indeed as the very embodiment of British identity. He began to perform this multi-purpose role in the wings, as a symbol of opposition to a corrupt government, yet by the end of the eighteenth century his place was secure at the heart of the nation's perception of itself. The people had become familiar with Alfred in their history books, as well as in literature, in art, and on the stage; and, as in the late ninth century, there was nothing like the reality or threat of foreign invasion to unite the people with their monarchy and with their government in opposition to a common enemy, and so to concentrate the collective mind.

Before the 1066 invasion what was considered "England" had been conquered by the Romans, Vikings, and other groups. It was more of a melting pot rather than a strictly homogenous society. The Romans built London, and the Vikings brought other innovations that carried over, etc. There was not one strictly homogenous culture, it was extremely complex with nobility marrying and inheriting lands in various places. Anglo-Saxons borrowed from the Normans and other neighboring groups, adding onto the cultural heritage already established through previous invasions. The Catholic Church was largely responsible for the flow of ideas and influence in the Middle Ages, through establishing monasteries as centers of learning (then dispatching monks and clergy throughout various regions).

The Loire Valley was a great center of learning in this period. Chansons or epic poetry flourished and expanded Franco influence to adjacent area's courtly customs. There was a fluid exchange of literary and social ideologies between the Normans and Anglo-Saxons during this period.

By the time of the invasion in 1066, there was a power vacuum and an unpopular Anglo-Saxon ruler. After William's victory, many living on the island easily adapted to the Norman leadership. There were already ties to this neighboring culture, and day to day life for the majority (laypeople) was not greatly impacted. Anglo-Saxon nobles may have lost power in certain situations or held on to their lands by proving loyalty to the crown.

The Bayeux Tapestry is a great indicator of the relationship between the Anglo-Saxons and the Norman invaders. Although not much is known about the origin of the Tapestry, many contend that Anglo-Saxon craftspeople worked to create the tapestry depicting the invasion in a favorable light. If Anglo-Saxon women were responsible for the creation of the Tapestry (its design was probably conceptualized by monks or a member of the elite) then it serves as an example of how Anglo-Saxons felt about the invasion and the narrative they sought to portray about the benefit of strong leadership, ie. William's heroic scenes in battle versus a treacherous Harold. The Tapestry scenes can be understood as a kind of propaganda, where the victor William the Conqueror and his retinue, including Bishop Odo, display valor and chivalric ideals contrasted by Harold's (the Anglo-Saxon) unfavorable qualities, which made him unfit to rule. William's legacy continues to this day as a kind of unifier among the various groups on the island under one strong monarchical rule (prior to this feudal lords would compete for various advantages). His reign established a powerful central leadership, which in my opinion is why the narrative of the invasion is viewed in a favorable light even today.

In short, "England" had a history of invaders that "took their land" and the Norman conquest likely would not have been met with hostility from the majority of laypeople. Feudal lords had the most stake in losing their lands, but many did acquiesce and sought stronger Norman leadership. Counter to what we think about the Middle Ages as the Dark Ages where societies became isolated and degenerated, this was a time of cultural exchange between neighboring nations due to the Church's influence over the region. Links between the nobility in these areas only complicated matters further. There were more connections between Norman and Anglo-Saxon societies than one might think.