The surname Bresinton was first found in Derbyshire at Brassington, a village and civil parish in the Derbyshire Dales district which dates back to the Domesday Book of 1086 where it was listed at that time as Branzinctun.  The place name literally means "estate associated with a man called Brandsige," from the Old English personal name + "-ing" + "tun."  Hence, conjecturally, the surname is descended from the tenant of the lands of Brassington, Henry de Ferrers, a Norman Baron who was recorded in the Domesday Book census of 1086. Henry was seigneur of St.Hillaire de Ferrers near Bernay in Normandy. 
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Migration of the Bresinton family
Some of the first settlers of this family name or some of its variants were: Thomas Brasington, who came to Virginia in 1622; Samuel Brassington, who settled in America in 1749; J. Brassington, who arrived in Baltimore in 1820.