Modern English people are descended from Angels, Saxons, Normans, Frisians, and Jutes. Would the majority of this ancestry Be Saxon though? Would Normal English people have More Saon ancestors than ancestors of any other sort? Genetically what group of people would modern English people be predominantly represented in the modern English genepool? Does it make sense to call Darwin or Newton Saxons in terms of descent and DNA?
Saxon refers to an ethnic, cultural, or political group -- not a set of DNA.
In late antiquity, there were lots of groups of barbarians, including the Saxons. These groups were, in most cases, very new. Some of them had older names (like the Goths), but their people came and went as these tribes formed new alliances with the Roman empire, fought against it, or were caught in the middle. In practical terms, this meant that most of the people who identified as Saxons (or Visigoths, or Vandals, or Huns, etc) didn't have Saxon ancestry stretching back for generations. Their grandparents probably identified as part of another barbarian confederation; their children, in many cases, did as well. Many of the Huns, for example, became Ostrogoths after Attila's confederacy collapsed, and many of their grandchildren became Italians or Romans or Greeks when the Ostrogoths were crushed; some, certainly, became Lombards a century later. Politics in the barbarian countries were dynamic, and ethnic groups came and went very quickly.
People did migrate from Saxony to England. How many is still contested -- maybe 10% of England's modern DNA came from these migrants, maybe as much as 40% -- possibly much less than either of these numbers. But these people didn't bring Saxony with them. Some cultural practices crossed the North Sea, others did not, and the people groups who emerged in England in the early middle ages didn't identify as the same people as those in Saxony. Some called themselves Saxons, but they were distinct kingdoms with distinct cultures and histories, and the 'Saxon' identity was more of a fiction -- an 'imagined community' -- than reality.
Modern Englishmen could call themselves Saxons if they wanted to. But that label is largely meaningless today. The Saxons were a people group of late antiquity who were wiped out by Charlemagne, and their children are spread across Europe as members of other cultures and other ethnic groups. Those of us who descend from English stock could just as easily identify ourselves as Iceni, Romans, Goths, Huns, Irish, Picts -- we've got all of them in our genes. But we're not really any of these people, because we're part of a different culture and ethnic group today.