Actually, the exponentiation of ancestry proves that Salazar is the ancestor of everyone in Great Britain by the pigeonhole principle, except in your case where each of his descendants only has one child. That is an extreme outlier and not likely to happen, all things considered.

A recent paper shows that everyone who lived in Europe 1000 years ago is an ancestor of everyone living in Europe today (barring immigration of course):

We can furthermore conclude that pairs of individuals across Europe are reasonably likely to share common genetic ancestors within the last 1,000 years, and are certain to share many within the last 2,500 years. From our numerical results, the average number of genetic common ancestors from the last 1,000 years shared by individuals living at least 2,000 km apart is about 1/32 (and at least 1/80); between 1,000 and 2,000ya they share about one; and between 2,000 and 3,000 ya they share above 10. Since the chance is small that any genetic material has been transmitted along a particular genealogical path from ancestor to descendent more than eight generations deep [8]—about .008 at 240 ya, and 2.5×10−7 at 480 ya—this implies, conservatively, thousands of shared genealogical ancestors in only the last 1,000 years even between pairs of individuals separated by large geographic distances. At first sight this result seems counterintuitive. However, as 1,000 years is about 33 generations, and 2^33≈10^10 is far larger than the size of the European population, so long as populations have mixed sufficiently, by 1,000 years ago everyone (who left descendants) would be an ancestor of every present-day European.

Great Britain is a lot smaller than Europe as a whole, so it probably takes even less than 1000 years for this effect to work.