We have put together a short survey to capture your feedback in terms of what BT can do when you experience home Wi-Fi issues. We would appreciate it if you could take a couple of minutes to complete a short survey. Read more from here, Fix my home Wi-Fi
If they don't find a fault you will not be charged but if they do find a fault on your side of the test socket you will be charged hence the reason to check for noise using the test socket.
If there is still noise using the test socket it means there is a problem on BT's side of the socket and it is their responsibility to get it fixed at no cost to you.
There should be no noise. As I have said, report a phone fault and when that is fixed your broadband will improve.