If OpenReach are installing FTTP without it being asked for then that's what's known as "native FTTP". There are no huge installation costs. Just standard activation fees like with any other product. It comes reasonably priced per month, with standard contact lengths.
Then there's FTTPod (FTTP on demand) or FoD (Fibre on demand). Both those can show as available on the BTw DSL checker, but they need to be ordered for the fibre to be installed. It can (and does) cost thousands for installation of the latter 2. The monthly cost is much higher than with native FTTP. There's also a 36 month minimum term.
Basically native FTTP is great, installed for free, sold as BT Infinity 3 & 4 (other ISP terms will vary). The on demand options cost thousands to install and over the contract period thousands more.
FTTP coming to an area doesn't really mean anything unfortunately. They could do the street next to you and totally miss your street. That would mean the on demand fibre options are your only choice.
Native FTTP is usually installed in areas where there is no FTTC available. Having access to FTTC means FTTP is less likely, though not impossible. Plans also change on a regular basis. If it was some time ago you were told FTTP was coming to your area and you've heard nothing since then don't hold your breath.
Very little of the country has OpenReach's native FTTP. Most of it is being deployed with BDUK funding. If your FTTC cabinet was BDUK funded then there's no real hope of getting FTTP.
