I was in exactly your position 14 months ago. Armoured copper cable and FTTP available. Openreach switched between a pole and ducting for a while. In the end they went with ducting but it took 8 months from available to order to a working installation.
As to who paid, I was with PlusNet. Openreach wanted to pass the £3k to them and they wanted to pass it on to me. In the end I went with BT because then magically the cost was absorbed. Not sure whether that was anti-competitive.
Infinity 2 over FTTP from BTBroadband