To clear the mud from the 2nd answer.... the WORD "Welsh" is indeed Germanic, it was the early English word for "foreigner". Typical piece of English arrogance, to call the Britons foreigners in their own country.
Brief history summary to clarify the previous answer and also respond to your question..... in the 5th century AD when the Roman legions left, Roman Britain remained a political unit, but under pressure from invaders, both Celtic and Germanic. The peoples of Ireland and of Britain beyond the Forth-Clyde valley Roman border were both Celtic. By 700 AD, political control of most of what is now England had fallen to the Germanic invaders ie the English, and the words "Cymraeg" in their own language and "Wealas" (Welsh) in English were in use to refer to the Britons and to their remaining kingdoms in western and northern Britain. The dark-haired olive-skinned Welsh of Wales today are the descendants of the Welsh of AD700.
But genetically the predominant inheritance of the English and the Scots of today is also that of the Britons. What makes the visible difference is the influx of Nordic immigrants. Geneticists reckon the number of Germanic settlers into England during the Anglo-Saxon conquest period is around 100,000 -- so maybe 5% of the population of what is now England at that time. The numerically larger influence was the Vikings, who came as raiders in the 9th century and then as colonists and rulers down through the 11th. The Viking impact was strongest in Scotland and in eastern England.
In addition, bear in mind the climate in Scotland promotes low-melanin skin. Wales is just as wet, but somewhat warmer on average.
There is no sign of a significant Roman influence on the British gene pool. But do bear in mind that the Irish culture says that the current people of Ireland are descendants of the "sons of Mil" who came from Spain. Genetic science does not contradict this legend.