They'll first listen to the line to see if they can hear the noise. I guess they'll then send an engineer to trace the noise and remake joints as needed. This is free of charge, it's why you pay phone line rental.

A final test, to avoid any possibility of it being your end, would be as recommended in the BT Phone Book. Which is to remove the faceplate of the master socket, and plug a corded phone into the test socket on the wall at the back, then do the quiet line test again. See this pic.

Fixing a voice noise fault is almost certain to fix the broadband fault, but mention broadband and you haven't a chance, as they go looking for the wrong thing.

In reply to a post by RobertoS:

A final test, to avoid any possibility of it being your end, would be as recommended in the BT Phone Book. Which is to remove the faceplate of the master socket, and plug a corded phone into the test socket on the wall at the back, then do the quiet line test again. See this pic.

Fixing a voice noise fault is almost certain to fix the broadband fault, but mention broadband and you haven't a chance, as they go looking for the wrong thing.

Thank you all so much for your help, it is hugely appreciated.