Relevant dates include 117 CE, when the Empire was at its greatest territorial extent, and the accession of Diocletian in 284. Irreversible major territorial loss, however, began in 376 with a large - scale irruption of Goths and others. In 395, after winning two destructive civil wars, Theodosius I died, leaving a collapsing field army and the Empire, still plagued by Goths, divided between his two incapable sons. By 476 when Odoacer deposed the Emperor Romulus, the Western Roman Emperor wielded negligible military, political, or financial power and had no effective control over the scattered Western domains that could still be described as Roman. Invading barbarians had established their own power in most of the area of the Western Empire. While its legitimacy lasted for centuries longer and its cultural influence remains today, the Western Empire never had the strength to rise again.
The end of Roman rule in Britain facilitated the Anglo - Saxon settlement of Britain, which historians often regard as the origin of England and of the English people. The Anglo - Saxons, a collection of various Germanic peoples, established several kingdoms that became the primary powers in present - day England and parts of southern Scotland. They introduced the Old English language, which largely displaced the previous British language. The Anglo - Saxons warred with British successor states in Wales, Cornwall, and the Hen Ogledd (Old North; the Brythonic - speaking parts of northern England and southern Scotland), as well as with each other. Raids by Vikings became frequent after about AD 800, and the Norsemen settled in large parts of what is now England. During this period, several rulers attempted to unite the various Anglo - Saxon kingdoms, an effort that led to the emergence of the Kingdom of England by the 10th century.
Hiberni (Ireland), Pictish (northern Britain) and Britons (southern Britain) tribes, all speaking Insular Celtic, inhabited the islands at the beginning of the 1st millennium AD. Much of Brittonic-controlled Britain was conquered by the Roman Empire from AD 43. The first Anglo-Saxons arrived as Roman power waned in the 5th century and eventually dominated the bulk of what is now England. Viking invasions began in the 9th century, followed by more permanent settlements and political change—particularly in England. The subsequent Norman conquest of England in 1066 and the later Angevin partial conquest of Ireland from 1169 led to the imposition of a new Norman ruling elite across much of Britain and parts of Ireland. By the Late Middle Ages, Great Britain was separated into the Kingdoms of England and Scotland, while control in Ireland fluxed between Gaelic kingdoms, Hiberno-Norman lords and the English-dominated Lordship of Ireland, soon restricted only to The Pale. The 1603 Union of the Crowns, Acts of Union 1707 and Acts of Union 1800 attempted to consolidate Britain and Ireland into a single political unit, the United Kingdom of Great Britain and Ireland, with the Isle of Man and the Channel Islands remaining as Crown Dependencies. The expansion of the British Empire and migrations following the Irish Famine and Highland Clearances resulted in the distribution of the islands' population and culture throughout the world and a rapid de-population of Ireland in the second half of the 19th century. Most of Ireland seceded from the United Kingdom after the Irish War of Independence and the subsequent Anglo-Irish Treaty (1919–1922), with six counties remaining in the UK as Northern Ireland.

Question: When did the empire that conquered the place that became England begin to fall?
Answer: in 376