Thanks for your response.
After I posted that message I thought my logrotate was working with my new password setup, however it was not. Just that the method I used to force logrotate into action to test it did not in fact copy the error messages to stdout.
After quite a lot of experimentation I decided that my setup was, for some odd reason, just not able to pick up the username and password from .my.cnf
I am now following the rather widely recommended suggestion to place both username and password in the actual invocation of mysqladmin from the logrotate script, ensuring that permissions keep the script safe from outside reads.
This too is a workaround :-( since it is not in accordance with the mysql helpfile. Finding the real reason why mysqladmin cannot get access to the contents of .my.cnf is on my list, but fairly low down on the priorities.