I had exactly the same problem a few weeks ago.
The BT engineer, whom I called in, quickly decided that it was likely to be a fault at the exchange. He went to the exchange down the road, quickly fixed the fault and returned to my house after about a quarter of an hour to check that everything was OK (which it was).
So I'm STRONGLY of the opinion that you'll need to contact BT. However please don't bother trying to phone them. The system only allows you to initiate an automated line check, with a promise that you'll be phoned back with the result or (if that's not possible) you can call again and select the 'update' option. The problem is that, when you call back, there's no 'update' option and you simply get invited to start the line test again!
The only way to actually report the fault is to go here:
http://www.bt.com/fault
Click on 'Check my line now' (because, once again, that's the only initial option).
Then, when the line is reported to be OK (as it almost certainly will be), follow the procedure for calling out an engineer.
Chris