I had exactly the same problem recently - it turned out to be due to dodgy internal wiring(I had done!). The wiring, although it worked was acting like an aerial and picking up 'crap' - I had even used cat5 twisted pairs.
I would suggest removing all internal wiring and adding it back one bit at a time to find out which bit is the issue.
The noise could also be due to a phone appliance so you had better remove those.
You are very fortunate that the line is clear at the BT side. This should really be fairly easy to solve through a process of trial and error.
Also note that crappy broadband appliances can introduce noise on the line - you will want to remove that when you are investigating - especially if youa re using an internal adsl card - you would not beleive the crap that comes out of pcs in the form of electrical noise.
Chris