So, does Summer Isle exist or not?

Does Summer Isle have another name? I have a pretty good map of Scotland and the Isles but it doesn't appear there...nor have I ever heard reference to it in any other book about the Hebrides.

Alternatively, what real island was the movie filmed on?   

My aunt told me that they say in Uist that Winston Churchill was secretly a Druid high priest who used to go there and participate in strange rituals...now there's a movie waiting to be made!