I own a silver Toyota Corolla saloon, and am having trouble removing some stubborn stains from the bodywork. My mechanic tells me they were most likely caused by sun-cream from hands and that they can't be removed!

The stains are shiny white and oily in nature and repeated car washes which are otherwise excellent have failed to remove them. If I try to scrub them off with a cloth they disappear for a few seconds then reappear. Is there a method you could recommend that would clean these stains off without damaging the paintwork?