Get Sky to arrange installation of a BT line -
"1.6 If you have chosen to take Sky Talk Line Rental and you do not have a BT compatible line, we may be able to arrange this for you and you will need to pay Sky a connection fee. We will inform you of our current connection fees at the time you book your installation. Sky Talk Line Rental customers do not need to pay any other provider for line rental."
Charges are levied by BT Openreach, providers then can choose how much to pass on to the customer.
Ofcom cap the amount BT Openreach can charge for connection @ £88 + VAT. BT has to provide telephony services to whoever asks for them unlike other providers who can pick and choose.
BT pay the first £3400 cost of a new line but as above can only charge the customer £88 + VAT. Considering many new lines will take decades before they run into profit at monthly rental of £11 it's not a bad deal and far from the "lining the pockets" falacy.
BT's 1571 is only free if you make 2 chargeable calls per month through their network. If you get calls through Sky use 1280 prefix to hop back to BT's network to make the necessary number of calls unless Sky have blocked access to this since upgrading their network.