OS X updater claims installation is successful, but new OS is not installed
This is the information I missed. I had downloaded a .dmg file, this installs the 'Install El Capitan' app (containing the full 5 GB installer) in the Applications folder. I was expecting it to install the OS instead.

The linked instructions show how to create a bootable installer on an external drive from the .dmg.


connect an external drive
Use the 'createinstallmedia' command in Terminal

sudo /Applications/Install\ OS\ X\ El\ Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ El\ Capitan.app


You can then boot the machine from the external drive and use it to update the OS on your normal boot volume. 

The drawback of this approach is that it erases the external drive.