Possible Early Cleveland Ancestors

According to "The genealogy of the Cleveland and Cleaveland families. An attempt to trace, in both the male and female lines, the posterity of Moses Cleveland ... [and] of Alexander Cleveland ... with numerous biographical sketches; and containing ancestries of many of the husbands and wives, also a bibliography of the Cleveland family and a genealogical account of Edward Winn of Woburn, and of other Winn families": this is a possible theory about who the early Cleveland ancestors were:

The Cleveland, Cleaveland family was founded, evidently, by Thorkil, in all probability a Saxon land-owner, who, it appears, at or soon after the time of the Norman Conquest, assumed assumed the surname de Cliveland, calling himself Thorkil 
de (of) Cliveland. 

His son Uctred de Cliveland, who was evidently the Uctred, the Saxon land-owner of 3 manors in the town of Ghigesburg and other possessions mentioned in Domesday [Doomsday] Book. Uctred gave land to the Priory. 

The English ancestry of the Cleveland emigrants to America 
is not yet definitely settled. 

The Parish Records of St. Nicholas Church, Ipswich, Eng. (printed 1897), show baptisms, burials, and marriages, 1542 to 1612, of ancient Ipswich, Eng., Clevelands, 
all of whom were unmistakably kin to Moses 1 Cleveland of Woburn, Mass., 1635-40... .

An updated and expanded version of the above information can be found here.