A study undertaken by archaeologist Silje Fretheim at NTNU’s Department of Archaeology and Cultural History suggests that Late Mesolithic dwellings in Norway were maintained and repeatedly used for a period of over 1000 years.
While the study correctly concludes that this continuity in use does not necessarily indicate a continuity of culture (as visible remains of houses in the landscape may have motivated their reuse), the continued use and occupation of dwellings that had been around for such a long time – and whose presence people would have been aware of for many generations – would certainly have been accompanied by ideas about the people who first built them, about their own relation to these people, and about the history of their environment.
Such ideas would have been passed on orally, and would have formed part of people’s cultural identity. While this does not imply a complete cultural continuum, it does suggest an awareness of history over a long time span – which would in itself constitue a degree of cultural continuity.
Evidence for cultural continuity in prehistory is not limited to the examples of this study, and I have noted similar cases in The Early Mesolithic Pendant of Star Carr: relatives across the sea and The First Humans in Britain: A Journey through Time
You can read more on Fretheim’s study here: Mesolithic dwellings: An empirical approach to past trends and present interpretations in Norway