If the inactive phone line put in by NTL, I think your choice is to either forget about the NTL line and get a new BT line or reactivate the NTL line and go with them for your BB.
However, you say you are looking for the cheapest BB ISP, which NTL are not, at £24.99 a month.
IMO, my ISP click here are the cheapest but they don't offer webspace or email addresses (only sending servers) with the service but then I don't need that. It depends what you want really. There are a few other ISP's offering sub £20 BB, Plusnet offer a limited service(no P2Por newsgroups) and Gio Internet but I can't vouch for them.
If you go the BT line route, check out click here and see what deals are on offer.