So the next challenge is to get at it, which means removing the kickboards, which means discovering that the cupboards have settled slightly and the gap has moved from "a close fit" to "well and truly jammed in". A careful application of unreasonable force solved that with only one more retaining clip being sacrificed, and I managed to extract the filter without flooding my kitchen (always a good thing to avoid). And yes, it was covered in fluff and nasty gunk, so that was all rinsed off and it now at least drains properly. With any luck it'll also wash my clothes properly now.
The final challenge was getting the kickboards back in - they did not want to go and I chipped a chunk of the veneer off. What I ought to do is get them out properly and sand/plane a few mm off the top of them, which will be an interesting exercise as they're made out of veneered chipboard. That, and trim the edges of the long one in front of the washing machine as it really doesn't need to extend 6 inches into both corners.
I'm also wondering if I can come up with a better way of fixing the kickboards as the existing clips keep disintegrating. Currently there's a springy plastic clip on the back of the board that clips onto the legs of the cabinets, which is all very well but it's as if they're purpose-built to shatter when you try and pull the board out unless you know precisely where the legs are. Screwing directly into the edge of the board is probably a bad idea, but I wonder if I could mount a block on the back of the board and then drop a long screw in from the base of the cupboard above? That would make removing them much easier as I can just take the screw out. There's the added complication that whatever I come up with needs to be reasonably hefty as it's got to stay put when attacked by a Roomba.