Removing the sleeve and the small additional grommet-type thing that sits in front of it didn't leave me any wiser: the shaft of the chuck still moves in and out, but even at its extreme inward position the tool doesn't lock.
Looking into the chuck I can see the lengthways raised strips which guide the tool in, but no visible locking mechanism - which I've discovered from an online search should be a ball bearing.
Does this mean that the entire chuck has to be replaced? Another quick search hasn't thrown up a source, but even if it had I suspect that it might be almost as expensive, and a great deal easier, simply to replace the whole thing. Am I right? Comparable budget models seem to be around for £50 or so.