A couple of earlier posts suggested the culprit might be PathFinder (can't say what the problem might be if you don't have PF, as all has worked fine since finding my solution).
In Pathfinder I deselected Start on boot AND (important) the next two buttons (menu bar and default browser), so PF doesn't reactivate on searches, etc. Make sure the desktop options in Features are all desected and that in the Finder interface all buttons are unchecked. For good measure relaunch the finder.
Then restart in Safe mode. Once there open Sys Prefs to change the desktop. Twice with this problem, at this point I found that even though the default desktop was on my screen only a question mark was in the first desktop setting. I set the one I wanted - the question mark was replaced by the correct image - and rebooted. All is well.
I haven't restarted Pathfinder, but assume that if I did and reverted to my usual settings I would find the same problem occuring with the new desktop.
For those with this problem who don't use Pathfinder, do you have any other Finder enhancement apps?
Hope the above isn't too confusing - but it worked for me.