Baret’s father, John, a minor Dorset gentleman, had taken a keen interest in parliamentary matters, attesting eight of the county elections between 1413 and 1437,
It appears that the Barets dabbled in trade: on 23 Mar. 1444 Henry and John Baret (either his father or brother) were granted licence to export skins called ‘moreyns’,
The date of Baret’s marriage to Anne or Amy Cammell, daughter of a Dorset landowner, is not known, although in April 1449 the couple were named first in the successive remainders of the Cammell manor of Burton Plecy in Northamptonshire, which they and Anne’s issue were to hold after the death of her grandfather John Cammell.
