John Gawdy was son to Sir William Gawdy (24 September 1612 – 18 August 1669), created 1st Baronet in 1663, of West Harling, Norfolk,[1] and his wife Elizabeth, née Duffield (died 1653), daughter to John Duffield of East Wretham.
Gawdy's other siblings were his younger brothers William and Framlingham, and his sister Anne.
He married Anne de Grey, the youngest daughter to Sir Robert de Grey (died 1644) of Merton in Norfolk, and his wife Elizabeth, née Bridon (died 1692).
After the Gawdy family moved to Bury St Edmunds following the death of his mother in 1653, he attended the studio of Matthew Snelling, a painter and miniaturist, and later that of Sir Peter Lely, deciding to become a professional portraitist.
He entertained the diarist John Evelyn who described Gawdy as "a very handsome person… and a very fine painter; he was so civil and well bred, as it was not possible to discern any imperfection by him".