Would be interesting to see the wording of the contract. A lot of contracts are potentially a minimum term that the customer agrees to rather than a binding contract that the supplier will provide it for the minimum term.
Would be interesting to see a legal viewpoint on whether the 12 month minimum terms are applicable to both sides or just to the customer.
The true construction of most contracts for telecommunications services imposes ongoing obligations on both sides, with a minimum period of service imposed on the consumer.
In this case, it sounds as if the original poster entered into a contract to amend the original contract for services. The terms certainly involved an obligation to pay a different (and lower) monthly charge, and likely imposed a new minimum contract period. The key thing here is that this amending contract appears to have been for an ADSL service, not the FTTC the original poster previously enjoyed.
It is unclear whether the switch to ADSL was a mistake on the part of the customer, who failed to understand what is clearly explained to him (which does not create any entitlement to leave the contract), or misrepresentation on the part of BT Retail, who might have claimed nothing would change in the type of service (which may well create an entitlement to rescind the contract).
The contractual position probably matters very little now, in that I'd expect any minimum contractual term for the ADSL brnadband service to be close to elapsing (unless it's more than a 12 month minimum). The main problem is the unavailability of FTTC, likely due to some sort of capacity issue at the cabinet.
If the problem is a lack of tie cable pairs and/or line card ports, this can be solved relatively easily and will likely be done in time. If the entire cabinet is full, it's either a case of hoping a second cabinet is installed or waiting until someone ceases their FTTC service.