of sharing telephone lines between two subscribers has been around for decades, and in the past was quite common - particularly in country areas. It was originally developed to overcome local shortages of equipment and/or exchange resources.
Nowadays the system is referred to as DACS, which stands for Digital Access Carrier System, and many subscribers have no idea that they are sharing a line with another person. The two subscribers can use the line at the same time, and normally there's no problem...........until one or both of them connects to the internet. That's when a degradation in line quality shows up - as it has in this case.
BT will tell you that they are under no obligation to supply a line service that's of data quality - their contract with all of us is to supply an analogue voice quality line service, and nothing else. That's the official position, but many people have found that if you speak to BT politely (but firmly) and explain why you need to have a standalone line they will often play ball and supply one. There's no guarantee of success, but it's worth making the enquriy