I had pretty much word for word this same issue. However I was really lucky and maintained a rolling contract, had them agree to pay for 2 months line and broad band subscription, then swapped immediately to a competitor. No noise on the line, internet doesn't drop every 30 minutes, and pretty much exactly the same product (but oddly slightly faster).

The only way I achieved this was with refusing to speak to tech support, instead constantly speaking to their accounts department. I was a bit miffed having to swap as I did recommend them to people, whilst they were good and affordable, however they had so many problems, especially recently I kicked them in the proverbial chuff.
(feedingtimeatthezoo day 1 of his bikini diet started, Thu 23 Feb 2012, 21:05, Reply)