Most Ancient Royal Family in all of the United Kingdom
It seems impossible to prove for certainy which is the oldest dynasty, due to the lack of written history and antiquity. It also depends on which written documents are to be BELIEVED, which is entirely subjective, regardless of what "historians" [there is very little consensus among historians] believe. They are still interpreting it according to their limited scope, which is, at best, journalism.
With that in mind, the Lebor Gabel Erenn, an ancient document used to establish lineage to ancient bloodlines, when combined with the Chronicle of the Picts, points to a bloodline that supposedly goes back all the way to Adam and Eve. I am personally not inclined to believe that directly, however, the more factual Chronicle of the Picts indicates a kingdom and a lineage, of which I can trace my origins, that arose around 2680 BC, descendants of Partholon.
Also, the oldest current noble family in the UK is Erskine. The name comes from a gaelic phrase, ar an sgain (upon the knife). Through matrilineal descent (it was a matrilineal line, even from antiquity), the Erskines are direct descendants one of the chiefs of one of the 7 founding tribes of Scotland, the Picts or Cruithne. They were called the Cruithne, after one of their first Kings, by the Gaels. Both Pict and Cruithne meant "painted" or "tattooed" people, due to the mysterious markings on their skin. Cruithne had 7 sons, who ruled the 7 tribes, and the land was named for these 7 sons. The region of Ce was renamed Mar, and so the ancient chiefs, called Mormaers, became the Mormaers of Mar. Through this, I am a direct descendant of Partholon, himself. According to the Lebor Gabal Erenn, The Book of the Taking of Ireland, Partholon was a descendant of Noah, and through him Adam.
There are a lot of pieces of the story missing, but this line has never ended, and I am living proof. So is the Countess of Mar and the current Earl (also means chief) of Mar.
It seems they are certainly the oldest surviving line, at least in the UK. But all we have is history, and the interpretation of history, which as mentioned is little more than journalism.