Try dialling 1470 17070 to make sure that your phone number has not been crossed with another line. You should hear your number spoken back to you.
Might this be part of the fault if the number has dropped off the phone routing system?
You can still get through on 0800 800 151, Option 1 and then wait to get to the desk.
As everything else seems to have been ruled out, it sounds like you have been marked as another service provider, this could either be on the BT Openreach systems (either just an error on the system or you have been slammed by another SP and will soon get bills from them as well) or on the BT Retail system.
If either 'computer says' your not with BT retail you wont be able to use 151.
It could also be an issue with BT's automatic system, but I guess not as your having a problem dialling (if the issue was with the robot it would say 'your not with BT call your SP').
I imagine this will be a bit of a nightmare to sort out, as BT Retail can only really see their systems and not Openreach's, so finding the problem will take them a while and then fixing it will take a lot longer.
Goodluck, you might need it