Under Yosemite (and presumably therefore El Capitan - and maybe some other versions of OS X) it is not possible to set automatic login if the System Password has been set to be the same as the Apple ID password!
I had, of course, tried unlocking the ASecurity & Privacy preference panel to allow me to uncheck the "Disable Automatic Login" box, but it remained greyed out.
Eventually I found the answer to the problem elsewhere in these Support Community pages. After the System Password had been changed the "Disable auto-login" box became unchecked and was no longer grey. I could then setup auto-login on the Users & Groups panel.
Thanks to everyone who helped on here and the other thread.