Genetic studies have shown that most people in England who aren't descended from recent immigrant populations have a large component of Anglo-Saxon ancestry because there's been so much mixing and internal migration over the centuries.

It's true that there have been many waves of immigration, but over time they mix so most of us can claim Anglo-Saxons, Jutes, Vikings, etc somewhere in the family tree.

The number of ancestors is exponential in the number of generations. Anyone whose ancestors lived in Britain at the time of those cultures will be descended from all of them.

Hence the smiley.