I use Abro® Headlight Restoration Polish.
It takes for ever to see any improvement by hand. You really need an electric buffing wheel.
T-Cut can remove deeper scratches.
But it isn't suitable for all plastics! You have to test an inconspicuous area first.
Roger (IBAISAIC on YouTube) recommends using a plastic restoration polish designed for perspex aircraft windscreens. It removes the dirt and oxidized layer, then fills the tiny fine scratches. Drying hard and clear.
In the USA you have a product called "Mirror Glaze". It looks like your equivalent to the aircraft polish.
