Just to finish the story. I contacted CISIS (email@example.com) on July 5th with a wall-of-text explaining my situation and a copy of this forum post. The following day I was emailed to say they had "accepted" my case. One week later I was offered fee-free termination plus 2 months credit, but I'd have to keep the service for another 30 days (thereby only really offering me one month credit). I've since had a couple of calls with very nice people trying to convince me to stick with Virgin and assuring me they can fix the problem, which I've politely declined. I am now running along quite happily with Plusnet and haven't had one dropped call since they took over the houses' internetting.
Thanks again to all of you that tried to help with this mess.