How bad is this level of interference?

Ouch, that's nasty. Probably an electrical thing, have you got anything like christmas lights plugged in? Old CRT TV? Live next to an electric train line?
Try unplugging / fuse breaking everything in the house (including lights) except for your laptop and the router, it should be easy to see if the graph stabilizes.
You can also try getting a portable AM/MW radio and tuning it to around 612KHz (middle of the adsl frequency range), move around the house with it and see if anything near the modem or the wall the cable runs through is giving off a lot of noise.
 
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