Just spent today doing the same after a stale odour started coming out of the vents (I don't use the air con that often). To access it was a little different to the pics posted up - for a '95 Terrano V6 auto, the release for the glove box is from the inside/side and just simply pops out allowing for the glove box to drop down completely exposing the two hinge screws for removal. Then the black backing plate consisted of 7 screws - 4 screws were similar to the pics posted but there were another 3 screws up around the glovebox latch area as the backing plate was a single unit extending right up to the latch.
However there wasn't really that much gunk inside but I did a vacuum anyway and cleaned as much of the build up on the coils.
Finally, got a Glade 3-in-1 disinfectant/deodoriser/sanitiser spray, put the air con on full and from the outside I blasted the spray into the external vents below the windscreen until I could smell the spray scent in the car. Also went through all the fan settings just to be sure that any germs built up in any of the vents over the last 18 years are history!