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Of course, but we are discussing the origin of names, including place of origin. Benjamin Disraeli, for instance, had a surname that originated in Italy. Most Jews who migrated to the UK in the modern era came with names not familiar to the natives.
The official version of British Jewish history has Jews, still without hereditary surnames, expelled from England in the Middle Ages. The later migration and settlement begins in the 17th century, as Jews from the Low Countries made their homes here. They were of Spanish origin and had names such as Lindo and Mendoza.

The distribution map of England and Wales for this surname in the ancestry.com site Marc has linked to shows a strong presence in South Wales. The Welsh adopted surnames much later than the English and sometimes under influences not in play in the medieval age. One such influence was evangelical religion which was influential in the 18th century, leading to the adoption of Old Testament baptismal names. This resulted in some unusual surnames among descendants of males so named. So we find surnames among the Welsh such as Emanuel, Habakkuk and Jehu. It's possible, I suppose, that Israel was another such name, so giving rise to the possibility of Israel as a surname of families of British origin.
When registration of Births was introduced in the UK (1840?) there were still Welsh people in remote areas using the literal patronymic - i.e., John, son Of Robert Williams would have been called John Roberts, not John Williams.