Dear Hootenanny
The word "whopper" was around when I was small (predating the American Burger King company) and meant, and still means, something very big. A frequent phrase is "that's a whopping great xxxx" (insert noun of your choice). Someone who tells lies is often accused of "telling whoppers", as in "whopping great lie". I have no idea how old the word is. The pronunciation of "Wapping" is identical to "whopping". So "whopper" may have come from "Wapping".That's why the story is around. Bodies washed over by the tide would have been bloated by the water and therefore very much bigger. They may well have been called "wappers".
I can't tell you where the information came from originally, but when I was living in Wapping (from 1980 - 2001) it was said to me quite frequently. We were amused that Burger King adopted the word. It may be fakelore, but it makes as much sense as anything else.