Like BOAC, I can use the full Outlook client (not Outlook Express) as a browser. It is not clear how independent it is of IE - certainly in my case I find that the browsing history in Outlook is identical to the copy of IE7 I occasionally use for testing. But it is a different executable, so that may explain why it has not been crippled alongside IE and Firefox.
The fact that this behaviour started for the OP on a network other than his own (possibly with no firewall), targeted web browsers to the extent that he can selectively no longer navigate to their websites while other sites (like PPRuNe) are accessible (albeit using a mail client as a browser), makes me think
MalWare.
LateArrival - until you can get the PC disinfected (or worst case, rebuilt), I would strongly recommend that you don't connect to the internet, and certainly don't conduct any online transactions, banking etc.
The full link to Malwarebytes is
Malwarebytes - you could try entering that (cut and paste) into the address bar of your mail client, rather than clicking on the link.
If you can get to it and download and run it, that should help. If the site is blocked, then it would tend to confirm it's a malware problem.
SD