Question: "What is British Israelism and is it Biblical?"
Answer: British Israelism, also known as Anglo-Israelism, is the belief that the "lost ten tribes" of Israel immigrated to Europe and then to England and became the primary ancestors of the British people, and thereby, the United States. British Israelism was made popular by the Worldwide Church of God and Herbert Armstrong...but other groups have held the doctrine as well.
Is British Israelism true and Biblical? In order to determine this, we need to examine the two primary claims: (1) The ten tribes were lost, and (2) The ten tribes immigrated to England.
(1) 2 Kings 17:18 states that Israel was deported to Assyrian in 722 B.C. After this time, mentions of the ten northern tribes (Israel) are rare in Scripture. However, other Scriptures (and historical records) indicate that some of the people of the northern ten tribes remained in the land. 2 Chronicles 35:18 records Israel celebrating the Passover with Judah approximately 90 years after the Assyrian deportation. It is likely that many people of the northern ten tribes fled to Judah to escape the Assyrians, and even more fled to the safety of Judah after the Assyrians had ransacked Israel. 2 Chronicles 15:9 records people from Ephraim, Manasseh, and Simeon settling in Judah long before the Assyrian invasion. In the New Testament, the prophetess Anna is said to be from the tribe of Asher (Luke 2:36), one of the supposed ten lost tribes. So, yes, many people from the northern ten tribes were deported to Assyria, never to be mentioned again. At the same time, there is sufficient evidence in Scripture to prove that the ten tribes were not lost, but rather in fact rejoined with Judah in the south. It is likely that when Judah was deported by the Babylonians, the people would have sought out the Israelites in Assyria (very near Babylon) and rejoined with them. In the returns to Israel recorded in Ezra and Nehemiah, the Scriptures nowhere limit the returnees as being entirely from the tribe of Judah.
(2) Is it possible that some of the deported Israelites immigrated to Europe, even England? Yes. It is likely? No. A journey from Assyrian to England would have been exceedingly difficult in ancient times, especially for a large amount of people. Geographically-speaking, Afghan-Israelism and even Japanese-Israelism have a greater possibility of truth. Further, why would Assyria, or later Babylon, or later Persia allow the Israelites to immigrate outside of their territories? Further, if the Israelites had the ability to immigrate, why would they travel to Europe / England instead of back to their ancestral homeland? So, while it is possible that some Israelites immigrated to Europe / England - it is highly unlikely that this occurred to any significant degree.
The primary goal behind British Israelism is to claim that England and the United States have inherited the covenant promises God made to Israel. While England and the United States have been blessed by God in many ways...it is not because God's promises to Israel have been transferred to those two nations. God's covenants with Israel always involved the specific land of Israel. Abraham's descendants would inherit the land. The blessings of God to Israel were always in connection with the specific land that was promised. These promises, therefore, cannot apply to England or the United States, as those two nations do not possess the promised land. Further, while a significant amount of Americans have English heritage, there are far more American immigrants combined from other nations than from England.
British Israelism (and other forms of Israelism) should be rejected because it does not have a solid basis Biblically, historically, or in reality.