If it is a vinyl top as you state, you will need a vinyl-specific cleaning product.
What you have not told us is how old the top may be and what condition is it in.
Is it a dull grey because dirt, road-traffic film, and/or natural debris like tree sap and pollen have become embedded in the vinyl top grain? Or do you have a specific area or areas that some type of stain that may be impossible to remove, like road tar specks or pine-tree sap that are on the top and have discolored the white vinyl?
My one suggestion is to use an Oxy-clean type cleaner to brighten the top first and get out the deep-seated gunk that may be graying the vinyl. OR use steam.I would not use a pressure washer, as this may force water into and between the seams and into the car, but you can decide this for yourself if you are more judicious in the pressure and where you point it.
One area that I find with older tops that are troublesome are the seams themselves. They tend to hold water and are fertile breeding grounds for mold and mildew. This is more true of canvas/fabric tops, BUT if this vehicle sits outside and is parked in shaded area, like carport without walls, the hot and humid summer temps can wreak havoc on tops if not properly cared for. I think that 303 makes a specific cleaner just for RV awnings to remove mold and mildew, but that RV awning material is more fabric-like than vinyl. I`ve used a stiff-bristle tooth brush and PLEASE don`t laugh, Mold Armor Patio Furniture Cleaner (WM Barr & Co. Inc.; Memphis,TN) to clean seams on a vinyl landau (fixed covering) roof top. It`s what I had on hand.
Let us know what specific cleaning problems you are facing with this particular white vinyl top and how you resolved them.
If you have problems, I am sure other Autopians will run into them as well, and we can all learn together.