Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
BASKETT
As described in historical dictionaries
Patronymica Britannica (1860)
BASKETT. Probably Fr. Basqnet, a diminutive of Basque, a native of Biscay ; a page or footboy, because the natives of that province were often so employed.
Surname type: Diminutive
Origin: English
Region of origin: British Isles
Country of origin: England
Religion of origin: Christian
Language of origin: English