Update: I tried all the suggestions!
The files shown on the list for a manual delete attempt didn't seem to be there. However, while I was working on the problem, my own AV programme (McAfee) suddenly updated itself. It then did something else (too quick to catch what it said) and the annoying little icon on the bottom of the screen was removed automatically and the false links to internet pages stopped coming.
However, the menu bar still showed links to suspect AV sites I didn't want to risk wasting money on.
Tarq, your SUPERAntispyware lived up to your recommendation! Having installed it, it immediately found 58 rogue items, now deleted. Things appear to be back to normal.
Thanks again for all your help!