Fixed phone I assume.
Your beef is with your supplier. That's who you contact. That they let BT connect the local link, is for them to moan at BT.
That stated BT still gets involved and if they aren't competent enough to find the error they will find a way to claim the issue is in your house somehow, and charge for the callout. So at the very least put a phone that you know is ok connected to the socket in the main box and confirm the issue is still there.
I suspect a dodgy connection or cable break is the most likely cause. These are intermittent and consequently difficult for BT to find and admit to.