I don't think you'd be able to find any evidence of your line being monitored (besides what you already describe making you suspicious that they are), as I highly doubt authorities would need to resort to using any on-premise devices to do that. A lot more likely scenario, assuming you are being tapped, is your ISP was issued a surveillance gag order in order to route your traffic that would normally pass your ISP's switch, instead through the network switch of whichever authoritative body is investigating your case, and thus gathering evidence without you being able to find any direct evidence of it, or your ISP allowed to disclose any information pertaining to ongoing investigation under threat of legal action against them, if they did (again, if at all this is the case).
Such gag orders are known to have been issued by courts in many countries in the interests of national security, including UK (see Wiki link above). The sudden drop in your ADSL line quality could as well be contributed to reconnecting your landline to a different switch, one that's possibly located further away than ISP's own switch is (ADSL lines are highly susceptible to the length that such connections need to travel through normal copper landlines). A few suggestion on how you could perhaps establish with less doubt your ADSL line is being or is not being tapped:
Check the contract with your ISP for any word on how fast are they supposed to respond to any reported issues with their equipment, ring them up and report problems with your ADSL line that you're experiencing. Then see if they respond at all, or if they do, for signs of avoiding disclosure. Tech guys ISPs send aren't really trained in dealing with their customers in covert ways, and their response alone might give you clues. If you had field technicians come to you previously (besides when you got connected), ask your ISP to send the same team, if possible.
When you're on the phone with your ISP reporting line issues, ask them to tell you the values of their qualitative measures of your line (distance to the switch, e.t.c.). Call them a few times at different times of the day until you get values from at least two call centre operators. It's likely disclosing such information wouldn't be covered in the gag order, if it was at all issued, and provided you have values to compare them to (compare to your closest neighbor's values, or to values from any previous service call, or maybe a field technician's report when you got connected?), you could maybe establish that the line is either indeed a different, or the same one that just happens to be picking up more noise for whatever reasons and is all a coincidence that can be explained otherwise.
I'll try to think of a few more ways, mind not all might apply in your case, I'm not UK based and such things might also be covered differently between ISPs themselves. Honestly though, if your line is being tapped, it's more likely it wouldn't be directly on the copper wire connecting you with the ISP's switch, but later redirecting your traffic to a different network, meaning there wouldn't be any noticeable difference on the ADSL line, at least not due to this cause. It is also quite possible somebody just moved something while your house was being searched, and some wires got partially disconnected in the process. It wouldn't be unheard of, my mom did that once, while searching for some old umbrellas in the hallway storage area, where the phone socket was installed. I say you call your ISP, report your problems, and see if they can make it work as it used to.