Hungerford was born in 1567 at Great Bedwyn in Wiltshire, the son of Anthony Hungerford of Down Ampney, Gloucestershire, a descendant of Sir Edmund Hungerford second son of Walter, Lord Hungerford (d. 1449) of Farleigh and Heytesbury. His mother was Bridget, daughter of John Shelley, and granddaughter of Sir William Shelley, justice of the common pleas. His mother was a devout Roman Catholic, and brought Anthony up in her faith.
Hungerford seems to be the Anthony Hungerford of Wiltshire, who matriculated from St. John's College, Oxford, aged 16, on 12 April 1583. Owing to his father's pecuniary difficulties he left the university within a year; but he is probably the Anthony Hungerford 'Armiger' who was created M.A. on 9 July 1594.
After much wavering in his belief Anthony Hungerford embraced the reformed religion in 1588, at the time of the Spanish Armada. He was knighted on 15 February 1608, and was deputy lieutenant of Wiltshire until 1624, when he resigned the office in favour of his son Edward. He settled at Black Bourton, Oxfordshire; died at the end of June 1627, and was buried in Black Bourton church.