Feedback for anyone else with the same requirements:
This turned out to be much more involved than I thought, for such a straightforward task. After downloading and testing the suggested free backup applications, I have to conclude that for my simple purposes, Karen's Replicator is still the best and most flexible. It is also the easiest to use, simply updates the previous backup each time rather than creating a new one or only backing up new or updated files, it deletes obsolete files from the backup, and once configured you can forget about it and just hit the relevant backup job title every so often to keep your files mirrored.
SyncBack apparently wouldn't copy open files, so it was a non-starter.
AllWaySync was too fancy, and seemed more suitable for synchronisation than for mirror backups -- it insisted on synchronising both the target and the destination drives so that old files were copied BACK from the destination as well as new ones being copies FORWARD to the destination. Possibly this could be configured, but it's a little too complex for a novice user who might be working on this computer.
FBackup was too inflexible, choosing and creating its own folders on the destination drive. There also appeared to be no way to specify an updating backup rather than a full one -- though again this might be possible by digging into the configuration, but it's still too fancy for a novice user.
Cobian looked to be the best of the recommended bunch with the most flexibility though novices will be baffled by all the options when first setting up a backup job. What I couldn't get it to do (and the Help file is not onboard, which is always an irritation) was to simply do like Replicator: update changed files in the original mirrored backup and delete files there which have become obsolete. It either wanted to make full fresh backups each time, or it wanted to create fresh directories with just the updated files, leaving obsolete files in the original mirrored backup undeleted and gradually building up to overflowing.
Replicator still wins for my simple purposes -- except that I still have a conflict with Office 2010. The search continues....