It would be true to say that, since 1066, all British monarchs have come from dynasties which either descended from the Norman dynasty that took power in that year, and made a claim to legitimacy based on that relationship (this applies even to usurpers such as Henry IV), or ruled territories outside the UK before they became ruler of England or Great Britain (as did William III and George I).

However the concept of "foreignness" is indeed problematic, for two reasons. One is that the Normans themselves (who were badly outnumbered in England, to the tune of around 10,000 invader-settlers to a native population of about 1.5 million) sought legitimacy and the collaboration of the conquered English by marrying into the Saxon royal line as early as Henry I (1100-35), whose first wife was Matilda, the daughter of Malcolm III of Scotland and the great-grand-daughter of the Saxon king Edmund Ironside (reigned 1016).

Moreover, owing to the importance of marriage as a political tool in this period, all major dynasties tended to contract marriages to "foreigners" and as such could be considered to a degree "non-native." A good example is that of Henry I's daughter Matilda – who was born to his Saxon consort, and was in turn mother of Henry II – who married the Holy Roman Emperor Henry IV and was known as the Empress Matilda in consequence. The same is also true of the "native" Saxon dynasty, which had a lot of Scandinavian blood. For example, the second wife of Æthelred the Unready, and mother to Edward the Confessor, was Emma, the daughter of Duke Richard I of Normandy – which is a big part of the reason William I had a claim to the English throne in the first place.

I think the concept of "foreignness" is problematic. How do you define it?