Annette:A good source is Rev. J. E. Jackson(1805-1891). His research papers are housed in the Wiltshire Society Library in Devizes.
He has Mary being the daughter of "an unknown woman" who was Edward Digby Gerard Hungerford's second wife. Edward's pedigree: Sir Edward (and Jane Digby); Anthony Hungerford (w/Rachel Jones); Sir Anthony Hungerford (w/Sarah Crouch); Sir Anthony Hungerford (w/Bridget Shelley); Sir John Hungerford (w/Bridget Fettiplace); Sir Anthony Hungerford (w/Jane Darell); Sir John Hungerford (w/Margaret Blount); Sir Thomas Hungerford (w/Christina Halle); Sir Edmund Hungerford (w/Margaret Burnell); Lord Walter Hungerford (w/Catherine Peverell); Sir Thomas Hungerford (w/Joan Hussey).