Update - A Virgin technician (Matthew) attended today. He decided to replace the set top box.
When it started it came on as an old (pre 360) system. Matthew explained this meant that the system must be logged on the Virgin database as not being upgraded to 360, which was clearly wrong.
After speaking to his manager to get the database updated he had to then install another new set top box. This loaded correctly and hopefully has solved the problem - time will tell if I stay logged into the Apps.
I am disappointed that none of the several call centre staff I spoke to noted this problem, as if they had I think a simple update of the database would have solved the problem.
I think this shows poor call centre staff training and a lack of attention to detail.