Final answer:
The Anglo-Saxons, from what is now southern Denmark and northern Germany, invaded the British Isles after the Roman withdrawal around 400 CE. Vikings from Scandinavia were also prominent invaders who settled in parts of Britain, impacting trade and culture from the late 8th century onwards.
Step-by-step explanation:
The tribes that invaded the British Isles were primarily the Anglo-Saxons, who were from areas that are now part of southern Denmark and northern Germany. Following the Roman withdrawal around 400 CE, these Germanic invaders filled the political vacuum left behind. The Anglo-Saxons included two distinct groups, the Angles and the Saxons, and they eventually merged into one cultural group referred to as Anglo-Saxons. They occupied and settled in southern Britain in the late fifth century and were responsible for the significant cultural shifts that took place there after the fall of Roman influence.
Another wave of invasion came with the Vikings in the late eighth century. Originating from Scandinavia, the Vikings began by raiding coastal sites in the British Isles but later settled in parts of England, Scotland, Ireland, and other areas across the North Atlantic. In 865, a Viking army invaded Britain and overthrew most of the Anglo-Saxon kingdoms, except for Wessex. These Norse settlers established trade and impacted the regional politics and culture significantly during their time.