Filtering of the mud has begun. I've removed large particles with a nylon vegetable bag I had lying around (one of those 'zero waste' ones you get in UK supermarkets but never end up using). Sediment filtering in water seems to be doing the rest of the work. The main difficulty, I think, will be drying the clay out given how damp everything in the west country is right now. Maybe boiling it on the hob at a low temperature is an effective way to remove the excess moisture?
I have no idea why I'm using my Thursday night after a day at work and a 3 hour commute to do this, but perhaps it's time to finally chase down that official autism diagnosis.