Hunter-gatherer populations from before the introduction of farming and herding of domesticated plants and animals to Western Europe makes up about 15% of the Western European maternal gene pool (represented in individual with mtDNA haplogroups U5a, U5b1, V and 3H). The finding is based upon both ancient DNA samples and mutation rate dating of mtDNA haplogroups.
This study doesn't estimate the Y-DNA contribution of European hunter-gatherer populations to the current Western European gene pool, but generally speaking, the patriline contributions of indigeneous men are similar to that of indigenous women or smaller. Thus, probably less than 15% of the total gene pool in Western Europe is traceable to pre-Neolithic hunter-gathers. By comparison, the non-African has 1% to 4% Neanderthal admixture.
Thus, even though there have been anatomically modern humans in Europe for about 30,000 years, and there were Neanderthals in Europe (who co-existed with modern humans in Europe for what may have been as much as a few thousand years) for a couple of hundred thousand years or so before that, about five-sixths of the Western European gene pool is attributable to population expansions of farmers and herders into the area in the last seven thousand years or so, although some of this "Neolithic wave" of population expansion may actually have been an Epi-paleolithic population that arrived in the region a few thousand years earlier and relied on fishing for food (and perhaps cultivation of non-domesticated plants) prior to the establishment of a truly Neolithic form of food production, converted culturally to becoming farmers, and then expanded in population.
Moreover, the hunter-gather population prior to the last glacial maximum in Europe around 20,000 years ago probably retreated to Southern refugia as the ice sheet advanced, only to return as the ice sheet retreated afterwards. There was not necessarily identity between pre-LGM and post-LGM modern human populations of Europe. The second wave of hunter-gatherer expansion into Europe could have been heavily infused with ethnically different people from SW Asia, for example.
The cultural connections of Western Europeans to the Mesolithic ancestors are probably even more shallow than their genetic ties to them.
In all likelihood, all of the languages of the Mesolithic human hunter-gatherers of Europe are extinct. If the Basque language is a Neolithic arrival (ca. 5,000 BCE in Iberia), and the Indo-European languages did indeed arrive in Western Europe only after this non-Indo-European substrate population had filled the region, and the Uralic languages of Northern and Eastern Europe arrived sometime after animals were domesticated in that area (probably after 6,000 BCE), then none of the extant languages of Europe can trace its origins directly to the Mesolithic peoples of Western Europe.
Uralic language speaking people have the highest frequencies of mtDNA haplogroup types associated with Mesolithic hunter-gatherers and were among the last to adopt full fledged farming as a means of food production in Europe, so it is possible that these languages might be a remote ancestors of an Eastern branch of the Mesolithic hunter-gatherers of Europe (which culturally and ethnically would have extended well into Siberian Asia), but there is no really strong evidence to support the description of Uralic languages as indigeneous back to the Mesolithic, rather than an intrusion that replaced prior languages during a Neolithic expansion.
Also, not all of the recent arrivals to Western Europe are associated with the first wave of Neolithic expansion in Western Europe. The first wave of Neolithic expansion in Western Europe appears to be strongly identified with the Neolithic Megalithic culture, popularly identified with Stonehenge although it appears to have origins in Portugal and to have stretched along most of the Atlantic Coast of Europe and the British Isles. This culture appears to have evolved mostly culturally rather than through population replacement into the early Bronze Age. Linguistically, it is common to associate with wave of expansion with a family of non-Indo-European languages that would have included the Basque language, which would have served the source of a "vasconic substrate" in Western Europe, upon which Indo-European languages of the area imposed themselves. There is likewise no good reason to suspect that the Caucasian languages pre-date the Neolithic revolution.
This first Neolithic wave, it was followed by at least two main waves of Indo-European expansions in the late Bronze Age and Iron Age which resulted in language shift, disrupted the local culture, and probably left a distinguishable genetic trace in contemporary Western European populations. The first wave of Indo-Europeans in Western Europe would have been Celtic or proto-Celtic and would have run its course, bringing all but a few pockets of Western Europe into the Celtic cultural sphere in the period from about 1250 BCE when Indo-Europeans first started to arrive, until about 500 BCE when they had largely asserted control even in the British Isles.
Several centuries after Celtic peoples consolidated control in Western Europe, the Romans would have arrived on the scene and conquered most of the same territory, only to lose its grip on those territories after the cultural transformation had already taken place when the Western Roman empire fell (one common date used to identify this moment is 476 CE, although the process happened in stages, rather than all at once). Christianity largely replaced Indo-European and non-Indo-European during the late Roman Empire and centuries of evangelization of areas beyond the boundary of the former Roman Empire during the Middle Ages that followed. Today, pagan folk culture, often incorporated into Christian rites, myths or secular rites, is all that remains, this often goes unrecognized as such, and these traces may be Indo-European rather than from the previous non-Indo-European cultural layer. While there are some relict pagan practice among the Mari of Russia and the Alevi of Turkey and Basque folklore (none of which are Indo-European linguistically), in Western Europe, all of the remaining pagans of "neo-pagan" having reinvented the dead religion from the vestiges of earlier days that they have been able to recover.
Iberia saw some demographic input from North Africa in the Middle Ages during its hundreds of years of Moorish occupation (on top of demographic inputs going both ways across the Straight of Gibralter dated to before the Neolithic revolution), but the populations genetic traces of the Middle Ages and early modern period in Western Europe were mostly internal to Europe (e.g. Viking invasions of coastal areas). There were also minor diasporic Jewish and Gypsy population migrations to Western Europe in that time period.
In Western Europe, the languages that descend from the Celtic languages are currently in a marginal position (Scotish Gaelic, Irish Gaelic and Welsh are the principal surviving Celtic languages and English is the dominant language in almost all of the areas where these languages are spoken with very few people being monolinguistic in Celtic). The predominant Indo-European languages of Western Europe are descendants of the Latin of the Roman Empire or are part of the Indo-European Germanic language family.
This experience appears to be typical of other parts of the world in Africa and in Asia that have developed agriculture. While population replacement of hunter-gather populations may not have been complete, the lion's share of the modern population arrives from relatively late arrivals.