The Picts were the topic of discussion on this week on In Our Time. They are a mysterious yet intriguing people because we don’t know much about them in their own words, but, they are one of the roots of modern Scottish identity. When I first encountered the Picts decades ago there was some debate as to whether they were a pre-Indo-European people or not. Today that seems to not be a hypothesis people entertain. Rather, the Picts were simply the least Romanized of the Brythonic Celtic people of Britain.
Today because of the genetic data I think we can be rather confident that by the time of the Roman Empire there were no non-Indo-Europeans left in Northern Europe. The Beaker people in Britain and Ireland seem to have overwhelmingly replaced the native population of farmers, whose ancestors had predominantly arrived from the eastern Mediterranean thousands of years ago (via the Atlantic littoral or Central Europe). Across Northern Europe, in general, the replacement of the previous populations was substantial, though not total.
In Southern Europe, the arrival of Indo-Europeans was more fitful, and persistence of Basque attests to the fact that non-Indo-European languages were spoken down to historical times (if Etruscan is considered native to the Italian peninsula, that’s another example, though this is hotly debated and I lean toward the exogenous model). The pre-Latin language of Sardinia was almost certainly not Indo-European, while Greek has a high proportion of non-Indo-European words in its lexicon.