I agree with the other comments, however I don’t think there are that many who they find have links to the aristocracy.
What I think the programme makers are usually chasing is just some kind of interesting back story, or to prove that a celebrities specific talent is passed down from a (possibly tenuous) link to ancestors who had a similar talent or interest. Eg musical, acting etc.
Any links to royalty or landed gentry are often recorded and some survive, which is why it is sometimes possible to get back further on those lines than with common folk.
Highly edited, highly contrived but a good watch nonetheless.