What ever the DNA mixand however universal, once communities are cut off from mixing with other groups, they start changing in minor ways to adapt specifically to their environment.
Darwin indicated that species could form by the evolution of one species splitting into two, or via a population diverging from its extant ancestor at a given point.
Thus the population of Britain, all genetically similar to those leaving to our east, could, when immigration slows down, begin to adapt certain genes to the conditions specific to where we live.
Darwins examples were finches living in the Galapagos Ilands, who colonised the islands as one species and then gradually developed 13 different species, all distinctly different as each changed in size colour, beak shape and so on to adjust to the habitat they found themselves living in.
The same presumably applies to people, so those living in Great Britain could become a distinctly different species, different from the original human stock they came from.