I’ve still no idea how they’ll get the cable across the hall and into the living room
Is the living room at the front of the property, sharing the same wall as the BT66 box shown in your photo? If so, as others have said, the installer will likely run the cable externally along the front wall to reach the living room, then drill a hole there to get it inside.
If the living room is at the back of the property (and you've said it's a mid-terrace), then the fibre would need to be run internally - clipped to skirting boards as you mentioned in a previous post. There's a limit to how far Openreach allow for this - 10m from memory, but I could be wrong - so if it's further than that you could be out of luck. In that case you'd need to agree a different internal location for the ONT (where the fibre terminates), which will need to have a power socket nearby. You could then run ethernet cable from here internally to wherever you want the Hub to be - it doesn't need to be next to the ONT, it can be up to 100m away connected by a Cat5e (or better) ethernet cable.