The indigenous British people migrated from Europe in prehistory, and share genetic markers with the people from northern Europe. In the thousands of years following this migration, people continued to move across the English channel with more or less regularity. So the British, like the rest of Europe, are products of thousands of years of genetic exchange with the rest of Europe.

The idea that people in different parts of Europe didn't racially mix until recent centuries is (excepting the opinions of a few Roman 'ethnographers' like Tacitus) a pretty recent notion, coming out of 19th century nationalism and the so-called 'scientific racism' of the late 19th/early 20th century. This idea of pure races of European peoples, while very important to groups like the Nazis for promoting a strong national identity, has little relationship to the reality of the pre-modern world, in which people moved around a surprisingly large amount.

One of the most recent methods for tracing people's migrations is to look at the stable isotopes in their teeth. When tooth enamel is forming during childhood, the unique isotopes in the ground water where the child lives will be trapped in the enamel. This can then be analyzed from excavated cemeteries, and reveals the region where the child grew up. This method has shown us many people who were buried far from their childhood homes. Pre-modern people got around, and no nation can claim to be 'pure bred.'