I've sorted it out! And it's a catch-22 situation.
Turns out that, in july, while trying to disable a nagging prompt IE8 presents on reopening, every time it's killed or when it crashes, I disabled "Enable automatic crash recovery" as recorded in the "Auto-"go to homepage" in IE8... Is there a way to do it?"
thread, which last post I quote below, for easy reference:
But now I've found the answer:
Go to Tools --> Internet Options --> Advanced --> Browsing and untick "Enable automatic crash recovery"
That suppresses the dialogue box, after IE crashes. And then it goes to the default homepage, as required.
I'm posting it here just for the record, so that others may find it, on searching.
And it worked OK for a while, then UOL made some "HTML Updates" to its pages and the crashes described in this thread began.
However, when I re-enabled "automatic crash recovery", the crashes still happen, but IE8 recovers from them seamlessy, so they are imperceptible, unless one causes the machine to really slow down. Hence, there's more to the "Enable automatic crash recovery" setting than the nag prompt I was keen on disabling, and it's really not advisable to untick it.
I guess it's best to put up with the occasional nag screen, than to use two browsers on a regular basis.
@Joseph_sw: True enough. Proxomitron can solve it, but I'd have to identify all offending tags, by trial and error...
In any case I'll look into it further, since I've been considering adding it to my setup for a long time already, and this may be a good time for it. Thanks for the suggestion.