Basil and mouldy fluff!

I reckon if the basil was wet when you covered it, plus the warmth from the propagator = ideal conditions for mould! Sounds as if you have a prettier mould than blue spotty mould.

Once the basil started going black, it was too late. Covering it in plastic only incubated the existing mold and matured it (the white stuff). You could try spraying a solution of 1 part white vinegar to 5 parts water to kill the mold, but it's rather like closing the barn door after the horse ran off. I think you'll still lose the basil since you're getting so much rain.