"Genetically, what proportion of the UK population is *not* descended from some immigrant?"
Also worth bearing in mind that the USA is barely 250 years old as a nation and from the point of view of the current "owners", barely 500 years old. The vast majority of USA residents are 4th generation or less.
Much of the Middle East as we know it today is the result of boundary drawing by Europe and the USA, splitting up "natural" aggregations and groupings of people into separate nations consisting of conflicting sub-groups. On the other hand, the Middle East is still very insular and tribal in it's outlook with much less sense of any national identity. A bit like the Balkans.