This suggested fix should be added to the list of actions that the Helpline people should ask when someone reports a noisy phone line but still have a perfect internet/broadband connction.
Q: Is the power to your phone coming via an extension power lead? Swap it with another one or plug straight into the wall socket.
I've just spent 20 mins with an OpenReach engineer trying to work out why my phone line was noisy. All checks passed clear but we still had problems even with a replacement phone. As I am an ex computer comms engineer we both understood this was a weird problem until we decided (in desperation) to remove the power lead and plug the phone into the wall,
Result: Problem solved.
Lots of devices need pwoer so there are many multi plug extension leads out there so I think this suggestion might be useful