In the book, the Shirley Eaton character (Vera Claythorne) steals Lombard's gun and shoots him dead. She then dreamily wanders into the house, sees the dangling noose waiting for her, and hangs herself. She is in fact guilty of the crime U.N. Owen accused her of, as were each of the eight guests.
U.N. Owen is the judge but does not reveal himself to Vera in the book. The boat that arrives on Monday finds 10 dead bodies. The crime is solved when the papers/memoirs of the judge (in which he Tells All) either wash up on the beach (a note in a bottle?) or are discovered in some way, some time after the fateful weekend. (The judge shoots himself after Vera's dead, but does it in his own bed so he looks like just another victim.)
It's a kick-*** book, but I can see that ending being problematic in Hollywood!
(I purchased a DVD of And Then There Were None, the first filmed version, fairly recently from Madacy, and it looks great. Highly recommended!)