The thing is
Digging up roads is expensive, if you already have the local conduits, then you have an advantage. You can't expect BT to allow others to put wires in their conduits, although doing it for them might be acceptable. There is a risk for BT that a third party will screw up a cable run and take out BTs cables in the process.
There is competition at the national trunk level, and even in larger cities where investment can be justified, but smaller conurbations just don't merit the huge investment in digging up the road. Look at the gaps in the cable TV network and you'll see where costs didn't match ROI on revenue. It isn't just digging up the road either, its negotiating the land access rights. Many cable companies, didn't connect houses that had no footpath or verge outside their property, or those on the wrong side of them, because they would have needed to reach a legal agreement with each land owner to dig up the front gardens.
BT had the wires there when the properties were built, or used telegraph poles. I doubt any cable company has thought of that, and if they have, the local authority would let them put up more.