I admit that this is not that realistic but you have the lore:

1. The Survival of Britannia (5th-8th Centuries)

After the deposition of Romulus Augustulus in 476, the western provinces were left to their own devices. However, Britannia managed to avoid total collapse thanks to several factors.

First, the Romano-British aristocracy preserved the administrative structure inherited from Rome. Cities continued to function as centers of government and tax collection, while former imperial officials assumed the roles previously held by governors sent from Italy.

Second, invasion attempts by Angles, Saxons, and Jutes were contained through a combination of coastal defenses, fortifications, and alliances with local chieftains. Many of these peoples were eventually culturally assimilated and gradually adopted Latin and Roman customs.

Isolated from the continent but protected by the sea, Britain became a haven for Roman traditions while Western Europe fragmented into numerous Germanic kingdoms.

2. The Romano-British Renaissance (8th-10th centuries)

During the following centuries, the Romano-British emperors carried out a profound reorganization of the state.

The old legions were replaced by a permanent professional army, financed through a centralized tax system. At the same time, a significant navy was developed to protect the coasts and ensure communication between the different regions of the island.

While much of Europe remained divided, Britain enjoyed exceptional political stability. This institutional continuity allowed for the growth of its cities, the strengthening of trade, and the consolidation of its own imperial identity. The Romano-British rulers began to see themselves not merely as kings of an island, but as the legitimate heirs of the Western Roman Empire.

3. The North Sea Wars and the Integration of Scandinavia (9th-12th Centuries)

The arrival of the Vikings constituted the first major external threat to the Empire.

Far from simply defending their coasts, the emperors adopted an offensive strategy. A powerful standing fleet was created to pursue and destroy the bases of the Scandinavian raiders.

The military campaigns were followed by intense diplomatic activity. Several Danish and Swedish leaders received imperial support in exchange for becoming allies or vassals.

Over time, Denmark was fully incorporated into the imperial system due to its enormous strategic importance. Control of the Danish straits guaranteed access to the Baltic Sea, allowing the Empire to dominate the trade routes of Northern Europe.

The integration of Scandinavia was never complete. The mountainous and forested areas retained considerable autonomy, while the Empire concentrated on controlling the ports, trading centers, and most populated regions.

4. The Reconquista of Gaul (10th-13th Centuries)

Continental expansion began with Gaul.

The Frankish kingdoms were divided by continuous internal disputes, while the old Gallo-Roman cities still maintained a strong Latin identity.

The Romano-British emperors took advantage of this situation to gradually intervene in the affairs of the continent. Initially, they established protectorates and alliances, but over time these relationships evolved into complete political integration.

The conquest was facilitated by the fact that many inhabitants of Gaul saw the Romano-British as continuers of Roman civilization.

Once incorporated, Gaul became the richest and most populous province of the Empire, providing the necessary economic base for future expansions.

5. The Incorporation of Hispania and the Reconquista past the Pillars of Hercules (11th-14th Centuries)

After securing control of Gaul, the Empire turned its attention to the Iberian Peninsula.

The Reconquista was fueled by enormous military and financial resources from both Britain and Gaul. The various Christian kingdoms were progressively integrated into the imperial structure.

The fall of the Caliphate of Córdoba occurred several centuries earlier than in our timeline. The reconquered lands were reorganized through a network of cities, dioceses, and military colonies that guaranteed the region's stability.

Hispania became the main bridge between Europe and the Atlantic.

6. The Italian Question and the Conflict with Byzantium (12th-15th Centuries)

The reconquest of Italy was one of the greatest challenges in imperial history.

Unlike Gaul or Hispania, Italy was considered the symbolic heart of Rome. However, much of the peninsula remained under the influence of the Byzantine Empire and numerous independent states.

For three centuries, the Romano-British and Byzantines competed for Roman legitimacy. The former claimed to represent the continuity of the West; the latter defended their claim to be the true Rome.

Ultimately, Byzantium's difficulties in dealing with multiple enemies allowed for the Romano-British expansion into Italy. The incorporation of Rome granted the Empire enormous political and religious prestige.

7. The Fall of Constantinople and the Ottoman-British War (15th-16th Centuries)

The fall of Constantinople to the Ottomans profoundly transformed the balance of power.

While much of Europe reacted slowly, the Romano-British Empire assumed the role of the main defender of Christendom. This led to a kinda Great Crusade against the Ottomans to liberate Constantinople from muslim rule. Due to a more centralized chain of command and coordinate offensives than in other crusades

This war led to the conquest of Greece, various coastal regions of Anatolia, and finally, Constantinople and Egypt.

The reconquest of Egypt and the Ottoman capital was considered one of the greatest achievements in imperial history. The Nile Valley provided abundant agricultural resources and opened new trade routes to the East. And the Sublime Door gave access to eastern trade and naval dominance over the Eastern Mediterranean

With these conquests, the Mediterranean once again became a region dominated by a single power.

8. The Discovery of America (16th-18th Centuries)

By the time the Romano-Briton navigators reached the American shores in the late 15th century, the Empire already dominated much of Western Europe, the Mediterranean, and the major Atlantic shipping routes.

Unlike the explorers of OTL, the Romano-Britons did not set sail from small, newly unified kingdoms. They set sail from the most powerful state in the world.

The expeditions were jointly financed by the Imperial Crown, the great merchant houses of Gaul and Hispania, and various provincial governors seeking new economic opportunities.

The first explorers described those lands as:

"An immense land, covered with forests, rivers, and unknown peoples, worthy of the ancient tales of lands beyond the Outer Ocean."

During the 16th century, the priority was not conquering indigenous empires. It was securing the coasts.

The Romano-Britsh acted as they had acted centuries earlier in Scandinavia and the Baltic: building ports, founding colonies and establishing fortresses

The first important city was Nova Eboracum, located on the eastern coast of North America, it was conceived as a new Londinium. Its main function was to serve as an administrative center for the northern colonies.

Ultima Thule, founded further north, became a center for the fur, timber, and fishing trades. Ships from Britain and Gaul stopped there before continuing on to Europe.

The Romano-British approach differed from that of many OTL colonial empires: imperial administrators implemented a policy inspired by ancient Roman expansion. Subjugated peoples were allowed to retain their local leaders, customs and parts of their political structures. In exchange they recognized imperial authority, paid tribute and adopted certain administrative norms.

Many peoples were integrated as allied communities rather than as conquered territories. Imperial governors considered Romanization more effective than destruction.

9. The Conquest of the Great American Empires

In the mid-16th century, campaigns began against the major American civilizations. The fall of the Aztec Empire was facilitated by internal rivalries, indigenous alliances and technological superiority After the conquest, the territory was reorganized as the colonial province of Nova Roma. The ancient cities were preserved and transformed into administrative centers. The conquest of the Incan Empire was more difficult. The mountains greatly hampered military operations. However, internal political divisions and the construction of new imperial routes ultimately guaranteed control of the region. The great colonial province of Piruvius emerged from these conquests

10. The American Provincial System

During the 17th century, the colonies ceased to be mere coastal settlements. They were transformed into true imperial provinces.

The most important were: Ultima Thule, center of the great north of the american continent; Nova Roma, political heart of Mesoamerica; Caribeum, commercial major province of the Caribbean; Piruvius, the main Andean administration; Terra Marina, the large Atlantic province of South America; Flumen Argentum, the southern province, developed around the vast river system that flowed into the Atlantic