Thank a lot for the responses. To clear up some of the questions in your posts...

The polarizer was circular, not linear.

I've shot 25 rolls of slide film prior to this one (all of them Kodachrome 64), but that's over a 13 year period so I'd have to admit that no, I'm not very experience at using slide film. However, aside from the occasional dud photo I haven't had this underexposure problem in the past with slides.

Yes, I should start taking more control from the camera, and I will, but 37 bad photos in a row has to mean it's an issue with the film or a fault with the metering. From reading your replies it seems it could be a combination of both.

I have some Kodachrome 64 in the fridge, so I have a plan! I'll run a roll through the camera, no filters, and see how that turns out. I'll also try Loren's suggestion with the grey card. If they turn out well-exposed then I can eliminate the camera as the problem and when I use Velvia again I'll experiment with it rated at 40, and maybe even slower.

I have some Velvia 100 as well waiting to be used. Is that a true 100, or does everyone agree that it should be rated at 80 as Loren says?

Thanks again for all your help.
Carl