BT (presumably BT Consumer and not BT Business. BT Retail no longer exists).
Well forgive me if I missed that most riveting news of bad getting even worse !
I therefore refer the honourable gentleman to my reply.
If Sky provide the broadband then Sky are responsible for getting it fixed when it goes wrong (even if they have to ask BT Wholesale or Openreach to do so on their behalf).
You of course still maintain your assumption that the fault is an ADSL fault not a copper fault ! What I said still applies 101% .... Sky cannot talk to BT Retailer/Consumer/whatever they decide to call themselves next week.