There are quite a few oral histories, rock carvings and pottery traces of the Sami people of northern Scandinavia. Some good sources can be found here http://www.helsinki.fi/~sugl_smi/senc/en/johdanto.htm Due to their isolation and relatively late assimilation to Scandinavian culture the Sami can be considered to be one of the best preserved cultures of a non-Indo-European origin in northern Europe today, since some of them still practice ancient rituals and speak their original language. It is difficult to tell just how old most of these rituals and vocabulary is, but they pre date the colonisation of Scandinavia by Indo-European tribes.
Further south we have the Funnelbeaker culture, which if memory serves me right is a very well researched example of pre-Indo-European culture in northern Europe, however I'll leave it up to someone else to explain the details of that.
Basque is the most spoken pre-Indo-European language at 720,000 speakers, in Europe.
To piggy back on this.. is there any stock to the idea that many southern Irish people are linked to pre indoeuropean ethnic groups? (IE: black Irish..)
I wonder if knowledge of this group died out with Irish nationalism, because only the diaspora seem to know about it.