Going back as far as Julius Caesar and Tacitus, it was noted that many of the inhabitants of the Western parts of Britain resembled the peoples of Spain (or Hispania, as it was then. Remember that this is before waves of Vandals and Berbers overran the country). The inhabitants of the east and south of Britain were big, red-haired people who resembled the Belgae from what is present day Belgium.

Although it is difficult to trace exact movements of populations during the "Dark Ages" after the fall of Rome, there appears to have been some inter-migration between Wales, Cornwall and Brittany, which explains why Welsh and Breton (and the extinct but reviving Cornish) languages have much in common. Likewise there was migration from Ireland to Scotland, which explains why Erse and Gaelic are similar.

Contrary to what AliUK and Bert have suggested above, that the UK is quite a melting pot for DNA, there is evidence that invading cultures (Anglo-Saxon, Viking) displaced the local population rather than intermingled. Here is a link to the BBC programme, Blood of the Vikings, which suggests that this was the case with the Vikings.

There is much resistance amoung people of non-British culture who have emigrated to the UK (I am thinking mainly of Indian, Bangladeshi and Pakistani people here), to losing any of their own cultural integrity. Thisk makes makes marriage between them and "native" Brits uncommon, at the moment anyway. This may well have been the case with mass immigrations in the past.