Well we eventually got the water softener replaced with a new one, and today SWMBO got fed up with the washing machine filling so slowly, so pulled it forward and disconnected the feed hose at the machine.
Lots of resin beads in the filter in the inlet, and behind that filter too (there seems to be another, fixed, filter inside the inlet). Flushed that out. After that, at the next wash it filled a lot more quickly. So grot in the filter was to blame. But why would a water softener leak resin beads?
Also, when I posted about this before, someone suggested that there may have been a pressure reducer at the machine inlet - a rubber disk at the end of the hose with only a small hole in it. In fact the hose has a plastic 90deg turn at the end, and that plastic turn itself is of narrow diameter.