I asked my ISP what BT had done to rectify the problem on my broadband and got the following answer:
BT had changed the SNR margin and applied interleaving to your line to try and reduce errors in transmission. This did not seem to fix the issue though. The way your service is now delivered has changed from BT exchange equipment to our own LLU equipment.
So, in other words, BT is now completely out of the loop (literally) and it works great!