Am I missing something or do I report it to BT?
I have also developed this same problem in the last few weeks. I have contacted BT who have tested the line and maintained three times that there is no fault on the line. I have also changed filters, moved the router (BT HomeHub 2) and phones and run all other tests suggested for establishing where the fault is. The only remaining option is to go back to my old router (Netgear DG834) but that doesn't seem to have worked for you.
Like you, my phone is very noisy and my broadband connection drops and my router occasionally reboots. The problem is intermittent for me but my connection speeds fluctuate all the time (more than expected) and my tested upload speed is now less than half, almost one third, of what it should be all the time. I will continue to plug away at BT to resolve this as everything points to an external problem.
Sorry I can't help at this stage. I can only suggest you do report it as the more people who do so the sooner it will be sorted out. So far I have only reported it to the broadband side so my next move is to try the phone line approach. I'll post if I get a result; perhaps you could as well.