Many thanks Vero!
I reset the permissions via Terminal, and then set them up again. As before, the other function keys that I've set to work with the Music app still do work (ie sound up, down etc) but the mute still doesn't. Debugger shows that the signal is being passed on (the top two are mute on F10, the bottom two are vol up on F12) and if i switch the commands, so that F10 turns the volume up, and F12 mutes, F10 then works in turning up the volume, and F12 doesn't mute the volume ... very interesting!
I'm on the latest OS, and Alfred is up to date (the latest was out just a few days ago).