If you are already connected as directly as possible to the incoming line there's nothing much else you can do. The problem is BT's responsibility and they have to deal with it (or well, Openreach).
Nonetheless it does sound like a fairly common fault your line has, though I can't name exactly what it might be - the folks over on TBB forums or Kitz may be able to tell you better.
If your internet would literally go off for days every time you made a phone call I'd be pushing seriously for compensation or or leaving. If you can afford it, AAISP are known for good service, they also offer to fix existing line problems for free if you migrate to them.
http://www.aa.net.uk/broadband.html