If you inspect the threaded part of the switch you should see a flat spot. The square washer fits the recess in the back of the dashboard and its center hole has a matching flat spot to the switch’s. The one inch nut adjusts the depth of fit so the bezel ends up flush with the switch at the front and the square washer keeps everything from spinning. In my car, this washer is cleanly stamped out so it appears that it was part of the original assembly and not some retro-fit. This is an original switch with Rootes keys.
If your problem persists it would be relatively easy to make the washer out of a piece of sheet metal. I think that this is the sure fire way to keep your switch from spinning. As you say, the switch’s nut cannot be reached with a wrench so it is adjusted by fitting and removing the switch until proper fit is achieved. I would think that at some time in the last forty years someone must have pulled out your switch and omitted replacing the washer on refitting.
My former Alpine had an aftermarket switch that needed re-tightening every time the car was hard to start. I learned to be gentle on the switch, something I never worry about with the Tiger…
Cheers, Gilles