From Basic access authentication: From Router Password Kracker: Test site for HTTP Basic authentication.
Firefox-specific info: Clearing "Active Logins" causes Firefox to delete its HTTP authentication cache. (Source.) Exiting Firefox does so also. Extension HTTP Logout does so also. Firefox doesn't provide a mechanism to delete an individual item in its HTTP authentication cache, although that's been requested.
I discovered that logging out of my old router does nothing useful ! It probably works correctly with some browsers but not with others.