Martin Cockburn was the son of Dr. Thomas and Rachel Moore Cockburn, of Jamaica. He settled in Virginia and owned an estate called Springfield, near Colchester. Cockburn served on the Truro Parish vestry from 1770 to 1779, and was later tax commissioner for Fairfax County. He was married to Ann Bronaugh.

In 1765, GW sold Cockburn 10,000 shingles (see Ledger A, 218).