Thanks for the comprehensive reply.
That sounded really promising - an issue with the shutter not opening properly at high light levels would certainly explain things. However, I've tried what you suggest - pointing the camera directly into a halogen lamp at a distance of a couple of inches, with the ISO set to 400.
The shutter is certainly opening under these test circumstances. I'm getting a flash of light through it every time - I even tried holding the camera various ways up to see if gravity had any effect (had an old SLR once where the mirror spring was weak and it worked much more successfully in "portrait" orientation, when it wasn't working against gravity to lift the mirror...)
Now, the only difference I can think of between shooting outdoors in bright light in summer and doing the test you just suggested with a bright light indoors is temperature. Perhaps the shutter is on the verge of sticking and on a warm day the blades expand ever so slightly and that's enough for it not to work reliably - whereas at my desk it's nice and cool and they move freely ???
Am I right in thinking the LCA doesn't have an aperture iris, rather the shutter can open at different apertures depending on the level of light?
I've just noticed something else strange too - when not in auto mode, ie using the aperture selector, apertures 16, 11 and 8 fire the shutter at quite a rapid speed, but apertures 5.6, 4 and 2.8 behave as if the camera is in a bulb mode - the shutter hanging open as long as the release button is held.... This can't be how it is supposed to work?! Electrical contacts need cleaning on the selector switch maybe?