Thanks, tschommer, I tried some of the suggestions in your reply, and found that by stopping the akonadi and nepomuk servers the original start-up sequence reappeared without the error message, although I still only saw one common wallpaper image. However, by going into the Desktops tag in System Settings/Virtual Desktops, I was able to re-tick the 'Different widgets for each desktop' check-box and then the full set of original settings was restored, apart from the KAlarm icon on the panel, which I have manually replaced.
I'm not out of the wood yet, though. After the re-start, although the akonadi and nepomuk servers are running again they seem to fail to engage with the system properly, since, KMail won't start up. The error message refers to failure to fetch a resource collection, and if I try starting KMail from the command line in Konsole, I get:
[peter_h@localhost ~]$ kmail
QDBusConnection: session D-Bus connection created before QCoreApplication. Application may misbehave.
QDBusConnection: session D-Bus connection created before QCoreApplication. Application may misbehave.
KGlobal::locale::Warning your global KLocale is being recreated with a valid main component instead of a fake component, this usually means you tried to call i18n related functions before your main component was created. You should not do that since it most likely will not work
[peter_h@localhost ~]$ kmail2(3808)/libakonadi Akonadi::SpecialCollectionsRequestJob::slotResult: Failed SpecialCollectionsRequestJob::slotResult "Failed to fetch the resource collection."
How do I get KMail back without losing my pre-existing message folders?
Also, the alarm setting options in KAlarm are all greyed out, so I can't reinstate the alarms I use.