The surname Egelefield was first found in Cumberland, England where one of the first records of the family was Robert of Eglesfield (d. 1349), founder of the Queen's College, Oxford. He was the son of John of Eglesfield and Beatrice his wife, and grandson of Thomas of Eglesfield and Hawisia his wife. "He was presumably a native of Eaglesfield, near Cockermouth in Cumberland, and is said to have been a bachelor of divinity of Oxford." 
Robert de Egglesfeld was listed as a Freeman of York in 1335.  He is presumably the same person as the previous entry with a different spelling which was typical of the times.
The first source continues "there was a Robert de Eglesfeld who had a grant made to him of the manor of Ravenwyke or Renwick, 1 Edw. III, which manor was subsequently given to Queen's College by the founder (see Hutchinson, Hist. of Cumberland, i. 212, 1794). Next year, 1328, Robert de Eglefield was elected knight of the shire for Cumberland (Parliamentary Accounts and Papers, 1878, xvii. l; Members of Parliament, p. 83). It is therefore possible that the founder entered holy orders late in life; for if there were two Robert Eglesfields, it is difficult to understand why the second is not named, where several are named, in the statutes of the college, especially since it was through this lay Eglesfield that it acquired the manor of Ravenwyke." 
Today Eaglesfield is a township, in the parish of Brigham, union of Cockermouth, Allerdale ward above Derwent, in the West division of Cumberland. Nearby is Eaglesfield-Abbey an extra-parochial place, locally in St. Mary's parish, city of Carlisle, ward, and E. division of the county, of Cumberland. 
Moving further north across the border into Scotland where many of the family now claim descent, it was "the name of a family of considerable prominence in Cumberland in the thirteenth and succeeding centuries. The name is derived from the lands (now village) of Eaglesfield near Cockermouth. Some notes with a pedigree, are given in the Transactions of the Cumberland and Westmorland Archaeological Society, new series, XVI, p. 241-247. A writ was issued to John de Eglisfeld in 1307 to levy 60 men from Cockermouth to pursue Robert de Brus (Bain, II, 1902)"