I can't find anything on the net that supports the theory that Hell's Kitchen (Clinton) was named after an area of London.
I have found several different sites stating that the exact origin is unknown. Most agree, that the name was originally a "knickname" derived because of the areas notorious and riotous past. And.... I found the following which suggests this knickname was originally attributed to a single house:
"...the decade of the 1870s saw a brawling rookery of a house at 39th Street and 10th Avenue give rise to the famous name of 'Hell's Kitchen,' which was to spread loosely over much of the West Side. Putting together the most plausible elements of the legend on its origin and use, I concluded that the name was first extended to the whole block over to 11th Avenue. It began supposedly with a rookie policeman standing with his usual partner observing a small riot on that block and saying, 'The place is hell itself.' The retort, from 'Dutch Fred the Cop' was 'Hell's a mild climate. This is hell's kitchen.'"
From: One Stop Above Hell's Kitchen, Sacred Heart Parish in Clinton, Henry J. Browne, Rutgers University 1977.