On Sunday I saw an engineer and working on a green cabinet several miles away and spoke to him briefly, he didn't know the details of my cabinets but said that they decide which exchange supplies which cabinet not based on the old exchange but where they can get infrastructure to. That seems bizarre when doing a check for fibre, that always refers back to the exchange.
The checkers all base their reports on the exchange your are currently connected to (by copper) simply because most people know and understand that reference. Nowadays, the checkers make explicit reference to the cabinet number too - because people are gradually coming to understand that this is important. It is also something we can see on the streets.
In the future, when we have only fibre, BT will not need as many exchange buildings. That is because the signal can get somewhere in the region of 5-8km over copper, but 20-30km in fibre. As a result, the fibre used for each cabinet only needs to go back to so many "head-end" exchanges, that can be sited further away.
In turn, that means the fibre spines, travelling out to the cabinets, don't always go in the expected direction.
Eventually - perhaps another 10-15-20 years - BT will be able to get rid of some of the small rural exchange buildings.
As for ducting ... there is a fairly good chance that ducting did already exist - at least as far as the cabinet, and likely on to the DPs on poles or in underground chambers.
Of course, if the fibre goes to another exchange, then it is likely that some of the path wouldn't have existing ducting - so it would depend what the cheapest way to add ducting would be. It might be cheapest for the fibre to go back towards the existing building, without going inside, and then follow existing junction or trunk cables back to a parent exchange.
The fibre itself will be within one or more multi-fibre cable fed through ducting, or more likely through empty sub-ducting which itself was pulled through existing ducting.
There has been some recent reports that suggests BT are trialling some new types of fibre, in order to cope with duct blockages better. However, I'm not sure we'll see that affect the spine work going on to each cabinet.
BT have maps of their infrastructure, but I wouldn't expect to see them online - it would count as a sensitive subject, security-wise.