I've had that!
For me, I had the (overhead)wire between my nearest pole and my house replaced.
On inspection I found two tiny nicks in the internal insulation - but all's well after having it replaced! *touching wood*
My provider Freeola/Entanet run tests and could see a fault - BT engineer visited and within the first 5 minutes he said "the fault's with your wiring"!
After pointing out a few FACTS he said - you're right it's outside somewhere...!
You say you're plugged into a BT face plate - to make sure you need to use the BT TEST socket
behind the removable faceplate!
For me rain made the situation worse. As soon as I picked up the ringing phone the connection stabilised. See if you can repeat the problem by ringing your own phone (with a mobile) and monitoring your router's statistics.