From the Dictionary of British Surnames by P.H. Reaney, pub. 1958, p. 107:

Egbert: Egbert, 1086, Domesday Book; Martin Egrebrith, 1279, Rotuli Hudredoum, 2 vols., 1812, Combridgeshire, Old English, Ecgbeorht; "Sword-bright"- a rare surname.
 

from British Family names & Their Origin & Meaning by Rev. Henry Barber, pub. 1968

p. 33 - Under Frisian Personal & Family Names - Egbert, Ebbert, Egberts, Egbers

p. 51 - Egbert listed in Domesday Book as holding lands

p. 59 - Egbert listed as Undertenants of land at Domesday Survey
 

from Index to Domesday Book

Egbert, Yorkshire ref. #2

As a family name, during this period of history, not much can be found in England. The family name did, however, flourish in the Frisian areas of The Netherlands.