Hello Milo et al, back from holidays now and have launched back into the problem again.
After numerous tries to disable add-ons, get rid of toolbars, run spy- and malware detectors etc, the issue was still recurring.
As I said, I greatly appreciate your help, Milo, but must still be doing something wrong as I can't get IE9 to stop freezing. It often seems to hang with a hugely long googleads.g.doubleclick.net address down the bottom, as if it's trying to redirect me somewhere but not getting there - this may have something to do with it.
However, I decided to try and bypass the hassle altogether and downloaded google chrome instead. Lo and behold, the clouds parted and it works quickly and hang-free. I'm happy for the moment, but will still try to ascertain if there's some nasty ware on our computer that still needs to be removed.
I contacted our security provider, Trend Micro, and they seem rather keen to find out what's going on - have sent them a log at their request and they have promised to get back to me with a fix. We shall see!
Cheers,
Tim