That sounds like you are in sync to the DSLAM, but failing to establish a PPPoE session with a BRAS and onwards to the ISP.
The echo requests are probably what the router uses to check that the current BRAS is still there. If it fails to hear a response, it gives up, and starts to create a new PPPoE session.
To start PPPoE, your router sends out a PADI message to find any BRAS that is willing to talk to it. The BRAS sends a PADO as a response, offering its services.
I think the process ought to then continue with the BRAS forwarding authentication information to your ISP.
Because it fails during PADI/PADO, rather than during authentication, it sounds like your connection is failing somewhere between the DSLAM, the Openreach Head-End and the BTW BRAS (as your ISP uses BTW), but it could be slightly later than that.