is of paramount importance, a noisy line will simply not support a digital data service. The issue here is that BT do contrct with you to provide a data service at all - the terms and conditions of your telephone line rental agreement only oblige BT to provide an analogue voice service.
As you have discovered, that means that you might not be able to have a broadband service, although your neighbours may well be OK.
Now if you were to have a noisy voice service, one that meant your phone calls were badly disrupted on a frequent but irregular basis BT would be obliged to fix the problem. You would need to phone them to report the problem of course.