If you haven't already, try the router and phone plugged into the test point behind the master socket (via a filter) with nothing else connected to see if the problem persists. Removing the lower panel of the master faceplate should disconnect all telephone extensions, thus eliminating them as a potential cause. Also try another router if you can borrow one, although it is unlikely to be the cause of the problem.
Sometimes when there is a high resistance fault, such as bad joint you can hear "modem" noise on the phoneline despite having a perfectly good filter (and a perfectly good router).
If you've previously made a note of your line stats from your router, you may find that the attenuation has increased or is varying and the SNR /sync rate has fallen or is very variable.
I've had this happen on my line at least a couple of times, including recently when BT were working on the lines to the exchange, fortunately BT fixed the problem (or it cleared itself) without me having to report it.
Unless you get a voice fault, such as line noise with the modem off, or a BT line test detects a problem then you'll probably have to deal with it as an ADSL fault and convince your ISP to send out a BT engineer.