Thanks sec_ware for your patience with this!

Some progress, at last. When I killed explorer and restarted it as administrator, your previous suggestions for opening Network Connections (and their properties) worked as they should. Needless to say, the desktop changed to that of the administrator and all open applications disappeared until I killed explorer and restarted it as the user with limited rights. It's a bit fiddly, but a lot quicker that formally logging out and logging back in with admin rights.

I recall reading something a while ago about the way that explorer runs and that may be relevant. I was less experienced (and willing to experiment!) then so I can't recall details - it went way over my head. I just wonder exactly WHY this behaviour is exhibited only with Network Connections. I guess that we, mere mortals, will never know the thought processes of the MS planners!