This Rolls-Royce advertisement appeared more than 55 years ago. Old though it is, it remains famous in many advertising industry circles. It was also helpful for Rolls' sales efforts in the United States.
Famed advertising man David Ogilvy was responsible for the classic advertisement. His Wikipedia entry is here and other biographical information is here.
This link has some background regarding the Silver Cloud. A cursory Google search did not turn up any information regarding who did the styling. Whoever it was, the task was tricky because of the requirement to maintain the traditional Rolls "tombstone" radiator/grille design while having the rest of the car's appearance reasonably up to date. That same problem remains to this day, the current solution being to have the grille conform more to the body shape.
I think the styling solution for the initial Silver Clouds was a good one (later versions were degraded thanks to the imposition of quad headlamps). The long hood and signature grille are retained, while the slightly dropped flow-back front fender and semi-separate rear fender give the car grace and lightness that would be missing if a slab-fender design was used. Also, the top features hints of razor-edge style, a nice echo of previous customized Rolls-Royces.
All things taken into account, I think the early Silver Clouds are the most successfully styled Rolls-Royces since 1955.
Here are two images of Silver Clouds that I found on the Internet, hoping the second one is a sales publicity shot. The Blue car is a 1956-vintage Silver Cloud and the other is a 1960 model Silver Cloud II.