The primary issue is getting the ISP (in your example BT) to take the problem seriously and recognise that it is something that Openreach can deal with. BT is not ***supposed*** to have better access to Openreach than other ISPs, but I'ms sure it does happen.
Having said that, large business that buy from BT (the sort with a multi-million pound annual spend) don't seem to have any problems in using BT ...