The 1841 Census shows that the Whitters are particularly well represented in Lancashire and Cheshire. However, before 1743 (the year in which Thomas Witter married in Parbold), there are only a few documents relating to the Whitters in Lancashire.
After tracing some family trees and evaluating and viewing various Parish registers, I personally believe that the Whitters in Nortwest England originally come from Cheshire and that this is the area of ​​origin of the surname in (Northern) England.
While some members of the Whitter family have always been in Lancashire over the centuries due to the geographical proximity of the two Counties, the majority (57 %) of Whitters in Lancashire 1841 descend from one single ancestor, Thomas Witter. Another 13% are also originally from Cheshire.
If my theory is correct that Thomas Witter was born in 1721 near Frodsham, Cheshire, than in 1841 at least 70% of the Whitters in Lancashire had their origin in Cheshire.

Based on my assumption that the Whitters from Lancashire are originally from Cheshire, I took a first look at the Parish Registers from 1538 to 1570  (Variants of the name used in the search: Whitter, Witter, Wytter, Whitta).

Parish registers were formally introduced in England and Wales on 5 September 1538 shortly after the formal split with Rome in 1534, when Thomas Cromwell, chief minister to Henry VIII, acting as his Vicar General issued an injunction requiring that in each parish of the Church of England registers of all baptisms, marriages, and burials be kept.

Between 1538 and 1570 there are 27 entries on baptisms, 17 on marriages and 21 on burials. Of this total of 65 entries, 54 are from Cheshire (83,08 %). Most of these are from Frodsham and Tarporley. The rest of the entries come mainly from various locations in the south of England.

Due to the scarcely existing entries in the Parish registers of Lancashire before 1743 and the strong concentration on Cheshire in the years 1538 to 1570, I assume that the surname Whitter, at least in the north of England, has its origin in Cheshire.
I cannot yet determine whether the surname developed separately in the south of England or whether the Whitters there also originated in Cheshire.

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For your further information you can find a list of Wills in Cheshire before 1700 here.