I can't tell if that looks organic (sort of looks like lichen?!) or like some sort of nasty chemical. How does it feel under your finger? Is it smooth or rough, does any dust come off?
I've scrubbed away at things before with no luck only to find a quick wipe with some Autoglym tar remover gets rid of it straight away. Not sure about using it on the plastic, though. Alternatively try some undiluted all purpose cleaner or some anti-limescale kitchen/bathroom clearer on it and see what happens.
Maybe try joining Detailing World and see if they have any suggestions?
Joe