This is excellent news!
The BT Voyager 2000 router was at fault. Getting a different code release installed on the BT router permits port 5060/SIP traffic.
It appeared to be blocking at the network level because the BT router was not showing the traffic as being blocked, as though it never got to the router. It was not a misconfiguration, just a (very nasty/ugly) bug in the BT router code.