I don't think the nisse has much to do with England, but as a Danish citizen, I know that the Nisse also is extremly common Christmas-related folklore in Denmark too.
One of the most popular Christmas TV shows and Christmas songs features these Nisse creatures.
Also they're typically either gift-givers or trouble makers in the household during December where small kids can get gifts from them and stuff like that.
I'm a bit rusty on this since we don't do this at my home since my family is Bosnian D: