Archery wasn't actively practiced in large scale and in doctrine in the Roman Empire until the prime of the East Roman (Byzantine) Empire, especially after their contact with the hordes of horse archers from the steppes.
What we call today the "Byzantine Empire" was in truth the Eastern Roman Empire that managed to survive several external barbarian invasions and internal discord, while the Western Roman Empire--which controlled Britain--did not survive. "Britannia" as the Romans called the province, was abandoned, and later came to be settled en mass by Angles and Saxons and Jutes who would later become known as "Angleish" or English today.
Meanwhile, the Eastern Romans persevered for another couple long centuries, before they eventially collapsed by Ottoman Turkic invasions.
It is worth pointing out that the "Byzantines" still called themselves "Romans" or "Romani" in Greek, despite no longer controlling Old Rome any more (thier capital of Constantinople was the "New Rome") and in dominant language changing from Latin to Greek.
