I've been having the same problem since Friday too - with particular sites usually, bbc, flickr, halifax.co.uk. I too have ruled out all of my kit. I managed to convince the guy from Virgin who came out to replace my TV box to replace the modem too, but no difference! If I browse using a neighbours virgin connection it's fine (with his permission of course), also if I use an IP blocker, that improves things considerably (pretty much sorts it). Could you try using the 'hidemyip' free trial (Google it) and let me know if it works for you? And where are you in the UK? I'm in Saltburn (midd ubr). If we can pin this down to being an IP blacklisting or routing problem that would be something (but weird.....?)
EDIT: using the Virgin proxy works too. Wonder what the tech guy meant by 'something is updating?'
PARANOID EDIT
: You don't, like myself, use (an SSL connection to) Newsgroups to download, ahem, tons of Linux distros and other legit stuff, do you?