David, it may be that the trigger part of your door handle has snapped, it's an alloy material with a steel pivot pin running through and failures are quite commonplace. Try and have a look at the reverse of the handle and see if there is an obvious crack. If so, your best bet would be to try and source either a second hand trigger assembly or a complete used door handle unit - new ones are around £200 and the trigger isn't available seperately.
If it's not the trigger then adjustment is limited because the inner latch mechanism is a sealed unit. Over time the grease in it dries out, new life can be breathed into an old mechanism by removing all the old grease and giving it a good clean, then regreasing. It's a right fiddly job removing the mechanism though.
If you need to change either the mechanism or the handle then you have to de trim the door, relatively straightforward but a bit time consuming.