The surname Thurrey was first found in "Kincardineshire and in Fife, but Torrie of that Ilk was seated in Dumfriesshire till their forfeiture in the reign of James III, who regranted to Thomas Carruthers the lands and church of Tony. " 
To the south in England the family descend from the castle and barony of Turry, Normandy. Not all of the family emigrated to England at the time of the Conquest as Henry and Richard de Tury, Turi, or Turri, occur in the Norman Exchequer Rolls of 1180-1195.
"Odo de Turri was a benefactor of Kenilworth Abbey in the time of Henry I.: and from this Odo, a man of large possessions in Warwickshire, Thoresby, in a detailed pedigree to be found in his History of Leeds, derives, in direct male descent, the existing family of Torre of Snydale (anciently Syndall) that bear Sable a tower Or within a bordure Vaire. They continued at Westwood in the county of Warwick till the end of the fifteenth or the beginning of the sixteenth century; we then find them in Lincolnshire; and finally, James Torre, living 1649-99, described as an eminent antiquarian, sold his property there, and acquired the manor of Syndale, still the seat of his posterity." 
"Other notices of the name are to be met with. In the Pipe Roll of 1189-90, I find Jordan de Turri, London and Middlesex; and Simon de Turri, in Notts and Derby. In 1261 Richard de Tur held lands in Aston-Clinton.—(Lipscomb's Buckinghamshire): and John de Tours or de Toury, in 1353, is mentioned in the same county, where their seat was Towersey.
A family "that gave as their arms a tower, were seated at Berwick in Dorsetshire, which their heir-general brought to the Russells."—Hutchins' Dorset.
John de Tours, who held of the Honour of Leicester, was a benefactor of Leicester Abbey; and 1232, Stephen de la Tour was a subtenant of the Lord of Belvoir. Isabella de Turs, probably his heiress, held in Thedingworth in 1296.—Nichols' Leicestershire.
It is not certain that these De la Tours, or those of Berwick, can be identified with the De Turris. But we may certainly include in the family Me de Turri, who in 1165 held a knight's fee of the Bishop in Worcestershire , and Stephen de Turs, a tenant of the Honour of Clare in Suffolk.