It appears that this problem is completely related to the Auto-login Check and Remember-me Check functions in the MySQLi Log In User behaviour.
I created the Log In User behaviour again, without those functions, and it's now successfully logging out users.
I have a "Remember Me" check box on my sign in page, which I'd like to use, although I have noticed that the same Remember Me check box for this forum has never worked so my faith in this facility isn't 100%!
I assume, if someone checks the "Remember Me" check box on the sign in page then when they access the login page again it should automatically log them back in? Or just pre-fill the sign in form?
I'd appreciate some advice on how this feature is supposed to work as it's obviously not in the help files.