I've rung NTL but, as expected, because my NTL account is working okay, they can't offer any help. What I did do was dial-up from both my affected computers to my NTL dial-up service and the emails from my work downloaded without any problem.
So that has got to mean that there is no problem with my settings or with any corruption with Outlook Express. Surely it must be something to do with my cable modem?