Scandinavian culture had a profound effect on Ireland - many of its coastal cities trace their origin to Scandinavian colonization. In the realm of folklore, in particular, the effect was extensive. I highly recommend the collection of excellent essays by the late Bo Almqvist, Viking Ale: Studies on Folklore Contacts Between the Northern and the Western Worlds.

Britain includes Scotland, so I imagine you're really asking about England. There, too, the Danelaw left an imprint on regional dialect, and many standard English words are of Scandinavian origin: words with the "sk" initial sound tend to be Scandinavian.