Gary,
If the GRP has ingrained dirt, then it sounds as if the surface has been affected by light and has become porous. The smooth top layer of the GRP moulding is called Gelcoat, it's a self coloured polyester resin about 1mm to 2mm thick, and the structural GRP body is under this.
You seem to have tried a really good, hard clean, but I think it's time for a repaint and there are two ways:
1. Buy a matching coloured Gelcoat - it's a twin pack of polyester resin and hardener - and apply with a fine roller unless you have a spray gun.
2. Use a GRP compatible yacht paint - like Toplac by International Paint - this is used for painting boat hulls above the water line - it's pretty tough stuff, weather proof, and is easier to apply.
In both cases you will need to prepare the surface (wet / dry paper to key the surface), and remove any trim or window rubbers before you paint.
Robert