Somewhere I read a suggestion that there was a specialist product used by the manufacturers and installers of plastic window frames for houses for cleaning the plastic after installation. I went to my local builders merchant and they had a PVCu Solvent Cleaner made by Everbuild which claims to remove ingrained dirt from PVCu and most other plastics. It is a solvent, so you will need rubber gloves, and it’s flammable as well. On eBay it’s available for under £10 for a litre bottle and it seems to do a good job in removing dirty marks, though Y10 is better where it comes to removing rust stains.
I’ve also used various caravan cleaning products for removal of black streaks, and prior to polishing the hull I’ve used another caravan product called “Silky.” Silky is pretty good at removing dirty marks as well as providing an initial polish to the hull before finishing off with Starbright Marine Polish, though the starbright stuff has doubled in price since my last purchased, so I might be looking for an alternative sometime soon.