Under “UK Census” you will find a list of the distribution of the name Whitter in England in 1841. It’s not complete, but only a list of the counties in which the name was most common: 1841 Census, England
A distribution map of the 1841 Census can be found here: 1841 Census Map

An even more detailed map and listing is available for Lancashire and Cheshire.
Based on this material, I am currently working on the family trees of these people.