FAO Alan:
I had a similar problem and after much faffing about and arguing with my ISP and BT I did the "Quiet Line Test" which involves disconnecting all extensions, unscrewing the front plate from the master socket, plugging a corded phone into the test socket (which sits behind the front plate) and dialling 17070 (Option 2). If you can hear the slightest bit of noise - at its worst like someone frying bacon! - there is a fault on the line. When I finally ignored the BT help (!) centre in Bangalore who repeatedly said "No fault on line" I called a BT engineer out. He did a quick check and within 10 seconds had agreed there was a fault on the line which, in his words, "would be enough to knock your broadband out". He rectified the problem in a couple of hours and I've had no problems since that time.