I have come across this on a different marque of car (Lotus) but could be the same issue. On that car the pushrod bore down on the back of the piston which was a concave recess. The rod onto the back of the piston needed a slight preload which was provided by adjustment at the pedal trunnion. If it did not have the preload the end of the rod would sit low in the back of the piston until the pedal was pressed. Pressing the pedal would then centre the pushrod against the concave face of the piston with an audible and “feelable” click. Not examined my Morgan pedal box and master cylinders in detail so may not be the same thing but they look like similar items.
