Edmondson was originally apprenticed to a barber, but afterwards became a coach-painter, and being much employed in emblazoning arms on carriages was led to the study of heraldry and genealogy.
When the baronets made an unsuccessful attempt to obtain some augmentation of their privileges, as appendages to their titles, they chose Edmondson as their secretary.
He died at his residence in Warwick Street, Golden Square, on 17 February 1786, and was buried in the cemetery of St James's, Piccadilly.
His extravagant manner of living prevented him from leaving any considerable property to his son, who continued the business of coach-painter till his death, which happened soon after that of his father.
A fine portrait of Edmondson, in his tabard and collar of SS., engraved by Bartolozzi, is prefixed to the first volume of the Complete Body of Heraldry.