I think I have resolved this by chance! A warning came up saying the trial to Norton Live Backup had expired. As we do not use this, I have uninstalled it. Lo and behold, the machine is not now continually trying to make connections when there is otherwise no activity on the machine. Quite why Norton would be doing this, or indeed why it was not showing network activity in performance manager, I am not sure, but hopefully the problem has ow gone away!
Another reason not to use Norton I guess.
MD